Almost All Finsler Metrics have Infinite Dimensional Holonomy Group

Name: Almost All Finsler Metrics have Infinite Dimensional Holonomy Group
Uploaded: 2020-09-24
Description: Abstract We show that the set of Finsler metrics on a manifold contains an open everywhere dense subset of Finsler metrics with infinite-dimensional holonomy groups.
Balázs Hubicska; Vladimir S. Matveev; Zoltán Muzsnay
{'id': 'https://openalex.org/W3089181035', 'doi': 'https://doi.org/10.1007/s12220-020-00517-9', 'title': 'Almost All Finsler Metrics have Infinite Dimensional Holonomy Group', 'display_name': 'Almost All Finsler Metrics have Infinite Dimensional Holonomy Group', 'publication_year': 2020, 'publication_date': '2020-09-24', 'ids': {'openalex': 'https://openalex.org/W3089181035', 'doi': 'https://doi.org/10.1007/s12220-020-00517-9', 'mag': '3089181035'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.1007/s12220-020-00517-9', 'pdf_url': 'https://link.springer.com/content/pdf/10.1007/s12220-020-00517-9.pdf', 'source': {'id': 'https://openalex.org/S6775291', 'display_name': 'Journal of Geometric Analysis', 'issn_l': '1050-6926', 'issn': ['1050-6926', '1559-002X'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310319900', 'host_organization_name': 'Springer Science+Business Media', 'host_organization_lineage': ['https://openalex.org/P4310319965', 'https://openalex.org/P4310319900'], 'host_organization_lineage_names': ['Springer Nature', 'Springer Science+Business Media'], 'type': 'journal'}, 'license': 'cc-by', 'license_id': 'https://openalex.org/licenses/cc-by', 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['arxiv', 'crossref', 'datacite'], 'open_access': {'is_oa': True, 'oa_status': 'hybrid', 'oa_url': 'https://link.springer.com/content/pdf/10.1007/s12220-020-00517-9.pdf', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5048014061', 'display_name': 'Balázs Hubicska', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I132735039', 'display_name': 'University of Debrecen', 'ror': 'https://ror.org/02xf66n48', 'country_code': 'HU', 'type': 'education', 'lineage': ['https://openalex.org/I132735039']}], 'countries': ['HU'], 'is_corresponding': False, 'raw_author_name': 'B. Hubicska', 'raw_affiliation_strings': ['University of Debrecen, Institute of Mathematics, Pf.\xa0400, Debrecen, 4002, Hungary'], 'affiliations': [{'raw_affiliation_string': 'University of Debrecen, Institute of Mathematics, Pf.\xa0400, Debrecen, 4002, Hungary', 'institution_ids': ['https://openalex.org/I132735039']}]}, {'author_position': 'middle', 'author': {'id': 'https://openalex.org/A5075594319', 'display_name': 'Vladimir S. Matveev', 'orcid': 'https://orcid.org/0000-0003-3053-5172'}, 'institutions': [{'id': 'https://openalex.org/I76198965', 'display_name': 'Friedrich Schiller University Jena', 'ror': 'https://ror.org/05qpz1x62', 'country_code': 'DE', 'type': 'education', 'lineage': ['https://openalex.org/I76198965']}], 'countries': ['DE'], 'is_corresponding': False, 'raw_author_name': 'V. S. Matveev', 'raw_affiliation_strings': ['Friedrich-Schiller-Universität, Institut für Mathematik, 07737, Jena, Germany'], 'affiliations': [{'raw_affiliation_string': 'Friedrich-Schiller-Universität, Institut für Mathematik, 07737, Jena, Germany', 'institution_ids': ['https://openalex.org/I76198965']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5014163504', 'display_name': 'Zoltán Muzsnay', 'orcid': 'https://orcid.org/0000-0003-4516-7261'}, 'institutions': [{'id': 'https://openalex.org/I132735039', 'display_name': 'University of Debrecen', 'ror': 'https://ror.org/02xf66n48', 'country_code': 'HU', 'type': 'education', 'lineage': ['https://openalex.org/I132735039']}], 'countries': ['HU'], 'is_corresponding': False, 'raw_author_name': 'Z. Muzsnay', 'raw_affiliation_strings': ['University of Debrecen, Institute of Mathematics, Pf.\xa0400, Debrecen, 4002, Hungary'], 'affiliations': [{'raw_affiliation_string': 'University of Debrecen, Institute of Mathematics, Pf.\xa0400, Debrecen, 4002, Hungary', 'institution_ids': ['https://openalex.org/I132735039']}]}], 'institution_assertions': [], 'countries_distinct_count': 2, 'institutions_distinct_count': 2, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': {'value': 2390, 'currency': 'EUR', 'value_usd': 2990, 'provenance': 'doaj'}, 'apc_paid': {'value': 2390, 'currency': 'EUR', 'value_usd': 2990, 'provenance': 'doaj'}, 'fwci': 0.418, 'has_fulltext': True, 'fulltext_origin': 'pdf', 'cited_by_count': 4, 'citation_normalized_percentile': {'value': 0.685757, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 77, 'max': 80}, 'biblio': {'volume': '31', 'issue': '6', 'first_page': '6067', 'last_page': '6079'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T13080', 'display_name': 'Finsler Geometry in Physics and Cosmology', 'score': 1.0, 'subfield': {'id': 'https://openalex.org/subfields/3103', 'display_name': 'Astronomy and Astrophysics'}, 'field': {'id': 'https://openalex.org/fields/31', 'display_name': 'Physics and Astronomy'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, 'topics': [{'id': 'https://openalex.org/T13080', 'display_name': 'Finsler Geometry in Physics and Cosmology', 'score': 1.0, 'subfield': {'id': 'https://openalex.org/subfields/3103', 'display_name': 'Astronomy and Astrophysics'}, 'field': {'id': 'https://openalex.org/fields/31', 'display_name': 'Physics and Astronomy'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T12287', 'display_name': 'Fibroblast Growth Factor Signaling Pathway', 'score': 0.9317, 'subfield': {'id': 'https://openalex.org/subfields/1312', 'display_name': 'Molecular Biology'}, 'field': {'id': 'https://openalex.org/fields/13', 'display_name': 'Biochemistry, Genetics and Molecular Biology'}, 'domain': {'id': 'https://openalex.org/domains/1', 'display_name': 'Life Sciences'}}, {'id': 'https://openalex.org/T10229', 'display_name': 'Optimal Transport in Geometry and Analysis', 'score': 0.9544, 'subfield': {'id': 'https://openalex.org/subfields/2604', 'display_name': 'Applied Mathematics'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/holonomy', 'display_name': 'Holonomy', 'score': 0.99515307}, {'id': 'https://openalex.org/keywords/manifold', 'display_name': 'Manifold (fluid mechanics)', 'score': 0.60717714}, {'id': 'https://openalex.org/keywords/finsler-manifold', 'display_name': 'Finsler manifold', 'score': 0.5641254}, {'id': 'https://openalex.org/keywords/finsler-geometry', 'display_name': 'Finsler Geometry', 'score': 0.559317}], 'concepts': [{'id': 'https://openalex.org/C32518243', 'wikidata': 'https://www.wikidata.org/wiki/Q907926', 'display_name': 'Holonomy', 'level': 2, 'score': 0.99515307}, {'id': 'https://openalex.org/C2781311116', 'wikidata': 'https://www.wikidata.org/wiki/Q83306', 'display_name': 'Group (periodic table)', 'level': 2, 'score': 0.6788707}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.62896353}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.6195178}, {'id': 'https://openalex.org/C529865628', 'wikidata': 'https://www.wikidata.org/wiki/Q1790740', 'display_name': 'Manifold (fluid mechanics)', 'level': 2, 'score': 0.60717714}, {'id': 'https://openalex.org/C177264268', 'wikidata': 'https://www.wikidata.org/wiki/Q1514741', 'display_name': 'Set (abstract data type)', 'level': 2, 'score': 0.6048013}, {'id': 'https://openalex.org/C169316501', 'wikidata': 'https://www.wikidata.org/wiki/Q2498782', 'display_name': 'Finsler manifold', 'level': 4, 'score': 0.5641254}, {'id': 'https://openalex.org/C184720557', 'wikidata': 'https://www.wikidata.org/wiki/Q7825049', 'display_name': 'Topology (electrical circuits)', 'level': 2, 'score': 0.35546285}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.32955816}, {'id': 'https://openalex.org/C121332964', 'wikidata': 'https://www.wikidata.org/wiki/Q413', 'display_name': 'Physics', 'level': 0, 'score': 0.22526047}, {'id': 'https://openalex.org/C114614502', 'wikidata': 'https://www.wikidata.org/wiki/Q76592', 'display_name': 'Combinatorics', 'level': 1, 'score': 0.19505388}, {'id': 'https://openalex.org/C41008148', 'wikidata': 'https://www.wikidata.org/wiki/Q21198', 'display_name': 'Computer science', 'level': 0, 'score': 0.18322557}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.1499944}, {'id': 'https://openalex.org/C12089564', 'wikidata': 'https://www.wikidata.org/wiki/Q1195879', 'display_name': 'Ricci curvature', 'level': 3, 'score': 0.10185385}, {'id': 'https://openalex.org/C62520636', 'wikidata': 'https://www.wikidata.org/wiki/Q944', 'display_name': 'Quantum mechanics', 'level': 1, 'score': 0.061411023}, {'id': 'https://openalex.org/C127413603', 'wikidata': 'https://www.wikidata.org/wiki/Q11023', 'display_name': 'Engineering', 'level': 0, 'score': 0.05105689}, {'id': 'https://openalex.org/C195065555', 'wikidata': 'https://www.wikidata.org/wiki/Q214881', 'display_name': 'Curvature', 'level': 2, 'score': 0.045812756}, {'id': 'https://openalex.org/C78519656', 'wikidata': 'https://www.wikidata.org/wiki/Q101333', 'display_name': 'Mechanical engineering', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C199360897', 'wikidata': 'https://www.wikidata.org/wiki/Q9143', 'display_name': 'Programming language', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 4, 'locations': [{'is_oa': True, 'landing_page_url': 'https://doi.org/10.1007/s12220-020-00517-9', 'pdf_url': 'https://link.springer.com/content/pdf/10.1007/s12220-020-00517-9.pdf', 'source': {'id': 'https://openalex.org/S6775291', 'display_name': 'Journal of Geometric Analysis', 'issn_l': '1050-6926', 'issn': ['1050-6926', '1559-002X'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310319900', 'host_organization_name': 'Springer Science+Business Media', 'host_organization_lineage': ['https://openalex.org/P4310319965', 'https://openalex.org/P4310319900'], 'host_organization_lineage_names': ['Springer Nature', 'Springer Science+Business Media'], 'type': 'journal'}, 'license': 'cc-by', 'license_id': 'https://openalex.org/licenses/cc-by', 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/2007.12396', 'pdf_url': 'https://arxiv.org/pdf/2007.12396', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'http://hdl.handle.net/2437/304151', 'pdf_url': 'http://dea.lib.unideb.hu/bitstreams/3bde8222-3286-4f3d-97e3-8bb060f54dae/download', 'source': {'id': 'https://openalex.org/S4306402089', 'display_name': 'University of Debrecen Electronic Archive (University of Debrecen)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I132735039', 'host_organization_name': 'University of Debrecen', 'host_organization_lineage': ['https://openalex.org/I132735039'], 'host_organization_lineage_names': ['University of Debrecen'], 'type': 'repository'}, 'license': 'cc-by', 'license_id': 'https://openalex.org/licenses/cc-by', 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, {'is_oa': False, 'landing_page_url': 'https://api.datacite.org/dois/10.48550/arxiv.2007.12396', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4393179698', 'display_name': 'DataCite API', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I4210145204', 'host_organization_name': 'DataCite', 'host_organization_lineage': ['https://openalex.org/I4210145204'], 'host_organization_lineage_names': ['DataCite'], 'type': 'metadata'}, 'license': None, 'license_id': None, 'version': None}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.1007/s12220-020-00517-9', 'pdf_url': 'https://link.springer.com/content/pdf/10.1007/s12220-020-00517-9.pdf', 'source': {'id': 'https://openalex.org/S6775291', 'display_name': 'Journal of Geometric Analysis', 'issn_l': '1050-6926', 'issn': ['1050-6926', '1559-002X'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310319900', 'host_organization_name': 'Springer Science+Business Media', 'host_organization_lineage': ['https://openalex.org/P4310319965', 'https://openalex.org/P4310319900'], 'host_organization_lineage_names': ['Springer Nature', 'Springer Science+Business Media'], 'type': 'journal'}, 'license': 'cc-by', 'license_id': 'https://openalex.org/licenses/cc-by', 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'sustainable_development_goals': [], 'grants': [{'funder': 'https://openalex.org/F4320320875', 'funder_display_name': 'Deutscher Akademischer Austauschdienst', 'award_id': '57447379'}], 'datasets': [], 'versions': ['https://openalex.org/W3044568232', 'https://openalex.org/W3089181035'], 'referenced_works_count': 23, 'referenced_works': ['https://openalex.org/W1494966128', 'https://openalex.org/W1511670827', 'https://openalex.org/W165894190', 'https://openalex.org/W1977875716', 'https://openalex.org/W1997671087', 'https://openalex.org/W2010240948', 'https://openalex.org/W2023441931', 'https://openalex.org/W2036309288', 'https://openalex.org/W2125498553', 'https://openalex.org/W2156744629', 'https://openalex.org/W218489606', 'https://openalex.org/W2400831887', 'https://openalex.org/W2488941658', 'https://openalex.org/W2801013814', 'https://openalex.org/W2962751343', 'https://openalex.org/W2962875629', 'https://openalex.org/W2995979020', 'https://openalex.org/W3080391065', 'https://openalex.org/W3101694757', 'https://openalex.org/W3105089014', 'https://openalex.org/W4230836784', 'https://openalex.org/W4242355477', 'https://openalex.org/W580207682'], 'related_works': ['https://openalex.org/W560877131', 'https://openalex.org/W4301915471', 'https://openalex.org/W4289752046', 'https://openalex.org/W3183650676', 'https://openalex.org/W2967056414', 'https://openalex.org/W2962751343', 'https://openalex.org/W2900665011', 'https://openalex.org/W2801013814', 'https://openalex.org/W2035492412', 'https://openalex.org/W2006502421'], 'abstract_inverted_index': {'Abstract': [0], 'We': [1], 'show': [2], 'that': [3], 'the': [4], 'set': [5], 'of': [6, 18], 'Finsler': [7, 19], 'metrics': [8, 20], 'on': [9], 'a': [10], 'manifold': [11], 'contains': [12], 'an': [13], 'open': [14], 'everywhere': [15], 'dense': [16], 'subset': [17], 'with': [21], 'infinite-dimensional': [22], 'holonomy': [23], 'groups.': [24]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W3089181035', 'counts_by_year': [{'year': 2023, 'cited_by_count': 1}, {'year': 2022, 'cited_by_count': 1}, {'year': 2021, 'cited_by_count': 2}], 'updated_date': '2024-09-26T08:16:45.264262', 'created_date': '2020-10-01'}
Publication Information

Video

Basic Information

Access and Citation

AI Researcher Chatbot

Primary Location

Authors

Topics

Keywords

Related Works
