A first integral for 𝐶^{∞}, k-basic Finsler surfaces and applications to rigidity

Patrick Foulon; Rafael O. Ruggiero
{'id': 'https://openalex.org/W2317890792', 'doi': 'https://doi.org/10.1090/proc/13079', 'title': 'A first integral for 𝐶^{∞}, k-basic Finsler surfaces and applications to rigidity', 'display_name': 'A first integral for 𝐶^{∞}, k-basic Finsler surfaces and applications to rigidity', 'publication_year': 2016, 'publication_date': '2016-01-20', 'ids': {'openalex': 'https://openalex.org/W2317890792', 'doi': 'https://doi.org/10.1090/proc/13079', 'mag': '2317890792'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.1090/proc/13079', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4210226894', 'display_name': 'Proceedings of the American Mathematical Society', 'issn_l': '0002-9939', 'issn': ['0002-9939', '1088-6826'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310315719', 'host_organization_name': 'American Mathematical Society', 'host_organization_lineage': ['https://openalex.org/P4310315719'], 'host_organization_lineage_names': ['American Mathematical Society'], 'type': 'journal'}, 'license': 'publisher-specific-oa', 'license_id': 'https://openalex.org/licenses/publisher-specific-oa', 'version': 'acceptedVersion', 'is_accepted': True, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': True, 'oa_status': 'bronze', 'oa_url': 'https://doi.org/10.1090/proc/13079', 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5070965544', 'display_name': 'Patrick Foulon', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I4387154239', 'display_name': 'Centre International de Rencontres Mathématiques', 'ror': 'https://ror.org/04e3d6y73', 'country_code': None, 'type': 'facility', 'lineage': ['https://openalex.org/I1294671590', 'https://openalex.org/I21491767', 'https://openalex.org/I4387153264', 'https://openalex.org/I4387154239']}], 'countries': [], 'is_corresponding': False, 'raw_author_name': 'P. Foulon', 'raw_affiliation_strings': ['Centre International de Rencontres Mathématiques-CIRM, 163 avenue de Luminy, Case 916, F-13288 Marseille - Cedex 9, France'], 'affiliations': [{'raw_affiliation_string': 'Centre International de Rencontres Mathématiques-CIRM, 163 avenue de Luminy, Case 916, F-13288 Marseille - Cedex 9, France', 'institution_ids': ['https://openalex.org/I4387154239']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5086771641', 'display_name': 'Rafael O. Ruggiero', 'orcid': 'https://orcid.org/0000-0003-3192-2596'}, 'institutions': [{'id': 'https://openalex.org/I2699952', 'display_name': 'Pontifical Catholic University of Rio de Janeiro', 'ror': 'https://ror.org/01dg47b60', 'country_code': 'BR', 'type': 'education', 'lineage': ['https://openalex.org/I2699952']}], 'countries': ['BR'], 'is_corresponding': False, 'raw_author_name': 'R. Ruggiero', 'raw_affiliation_strings': ['Departamento de Matemática, PUC-Rio, Rua Marqués de São Vicente 225, Rio de Janeiro, Brazil, 22453-900'], 'affiliations': [{'raw_affiliation_string': 'Departamento de Matemática, PUC-Rio, Rua Marqués de São Vicente 225, Rio de Janeiro, Brazil, 22453-900', 'institution_ids': ['https://openalex.org/I2699952']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 2, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': 0.12, 'has_fulltext': True, 'fulltext_origin': 'pdf', 'cited_by_count': 9, 'citation_normalized_percentile': {'value': 0.7814, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 85, 'max': 86}, 'biblio': {'volume': '144', 'issue': '9', 'first_page': '3847', 'last_page': '3858'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T13080', 'display_name': 'Advanced Differential Geometry Research', 'score': 0.9998, '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': 'Advanced Differential Geometry Research', 'score': 0.9998, '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/T10229', 'display_name': 'Geometric Analysis and Curvature Flows', 'score': 0.9783, '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'}}, {'id': 'https://openalex.org/T12924', 'display_name': 'Dermatological and Skeletal Disorders', 'score': 0.9567, 'subfield': {'id': 'https://openalex.org/subfields/1311', 'display_name': 'Genetics'}, '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'}}], 'keywords': [], 'concepts': [{'id': 'https://openalex.org/C11413529', 'wikidata': 'https://www.wikidata.org/wiki/Q8366', 'display_name': 'Algorithm', 'level': 1, 'score': 0.64892924}, {'id': 'https://openalex.org/C2776321320', 'wikidata': 'https://www.wikidata.org/wiki/Q857525', 'display_name': 'Annotation', 'level': 2, 'score': 0.5546773}, {'id': 'https://openalex.org/C154945302', 'wikidata': 'https://www.wikidata.org/wiki/Q11660', 'display_name': 'Artificial intelligence', 'level': 1, 'score': 0.4569481}, {'id': 'https://openalex.org/C41008148', 'wikidata': 'https://www.wikidata.org/wiki/Q21198', 'display_name': 'Computer science', 'level': 0, 'score': 0.4568731}, {'id': 'https://openalex.org/C2777299769', 'wikidata': 'https://www.wikidata.org/wiki/Q3707858', 'display_name': 'Type (biology)', 'level': 2, 'score': 0.43887046}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.34581345}, {'id': 'https://openalex.org/C127313418', 'wikidata': 'https://www.wikidata.org/wiki/Q1069', 'display_name': 'Geology', 'level': 0, 'score': 0.09638351}, {'id': 'https://openalex.org/C151730666', 'wikidata': 'https://www.wikidata.org/wiki/Q7205', 'display_name': 'Paleontology', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 1, 'locations': [{'is_oa': True, 'landing_page_url': 'https://doi.org/10.1090/proc/13079', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4210226894', 'display_name': 'Proceedings of the American Mathematical Society', 'issn_l': '0002-9939', 'issn': ['0002-9939', '1088-6826'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310315719', 'host_organization_name': 'American Mathematical Society', 'host_organization_lineage': ['https://openalex.org/P4310315719'], 'host_organization_lineage_names': ['American Mathematical Society'], 'type': 'journal'}, 'license': 'publisher-specific-oa', 'license_id': 'https://openalex.org/licenses/publisher-specific-oa', 'version': 'acceptedVersion', 'is_accepted': True, 'is_published': False}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.1090/proc/13079', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4210226894', 'display_name': 'Proceedings of the American Mathematical Society', 'issn_l': '0002-9939', 'issn': ['0002-9939', '1088-6826'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310315719', 'host_organization_name': 'American Mathematical Society', 'host_organization_lineage': ['https://openalex.org/P4310315719'], 'host_organization_lineage_names': ['American Mathematical Society'], 'type': 'journal'}, 'license': 'publisher-specific-oa', 'license_id': 'https://openalex.org/licenses/publisher-specific-oa', 'version': 'acceptedVersion', 'is_accepted': True, 'is_published': False}, 'sustainable_development_goals': [], 'grants': [{'funder': 'https://openalex.org/F4320322892', 'funder_display_name': 'Centre National de la Recherche Scientifique', 'award_id': None}], 'datasets': [], 'versions': [], 'referenced_works_count': 13, 'referenced_works': ['https://openalex.org/W1522722022', 'https://openalex.org/W1589013121', 'https://openalex.org/W1975697879', 'https://openalex.org/W2040635624', 'https://openalex.org/W2061130210', 'https://openalex.org/W2072247497', 'https://openalex.org/W2096181459', 'https://openalex.org/W2149849639', 'https://openalex.org/W2246382613', 'https://openalex.org/W3033228470', 'https://openalex.org/W4230748309', 'https://openalex.org/W4244768794', 'https://openalex.org/W63650605'], 'related_works': ['https://openalex.org/W4391375266', 'https://openalex.org/W2625833328', 'https://openalex.org/W2392921965', 'https://openalex.org/W2377979023', 'https://openalex.org/W2361861616', 'https://openalex.org/W2358755282', 'https://openalex.org/W2263699433', 'https://openalex.org/W2218034408', 'https://openalex.org/W2007980826', 'https://openalex.org/W1979597421'], 'abstract_inverted_index': {'We': [0], 'show': [1], 'that': [2, 78], 'a': [3, 45, 131], 'compact': [4], '<inline-formula': [5, 46, 95], 'content-type="math/mathml">': [6, 47, 96], '<mml:math': [7, 48, 97], 'xmlns:mml="http://www.w3.org/1998/Math/MathML"': [8, 49, 98], 'alttext="upper': [9, 50, 99], 'C': [10, 51, 100], 'Superscript': [11, 52, 101], 'normal': [12, 53, 102], 'infinity">': [13, 54, 103], '<mml:semantics>': [14, 55, 104], '<mml:msup>': [15, 56, 105], '<mml:mi>C</mml:mi>': [16, 57, 106], '<mml:mrow': [17, 58, 107], 'class="MJX-TeXAtom-ORD">': [18, 59, 108], '<mml:mi': [19, 60, 109], 'mathvariant="normal">∞</mml:mi>': [20, 61, 110], '</mml:mrow>': [21, 62, 111], '</mml:msup>': [22, 63, 112], '<mml:annotation': [23, 64, 113], 'encoding="application/x-tex">C^{\\infty': [24, 65, 114], '}</mml:annotation>': [25, 66, 115], '</mml:semantics>': [26, 67, 116], '</mml:math>': [27, 68, 117], '</inline-formula>,': [28], 'k-basic': [29, 81, 140], 'Finsler': [30, 82, 141], 'surface': [31], 'without': [32], 'conjugate': [33, 163], 'points': [34], 'and': [35, 151], 'genus': [36, 85], 'greater': [37, 86], 'than': [38, 87], 'one': [39, 88, 143], 'is': [40, 44], 'Riemannian.': [41, 90], 'This': [42], 'result': [43], '</inline-formula>': [69, 118], 'version': [70], 'of': [71, 126, 130, 138, 144, 148, 155, 162], 'the': [72, 94, 128, 135, 145, 153, 160], 'fact,': [73], 'proved': [74], 'by': [75], 'G.': [76], 'Paternain,': [77], 'analytic,': [79], 'compact,': [80], 'surfaces': [83], 'with': [84], 'are': [89], 'The': [91], 'proof': [92], 'in': [93], 'case': [119], 'relies': [120], 'mainly': [121], 'on': [122], 'two': [123], 'facts:': [124], 'first': [125, 132, 157], 'all': [127], 'existence': [129], 'integral': [133, 158], 'for': [134], 'geodesic': [136], 'flow': [137], 'any': [139], 'surface,': [142], 'main': [146], 'contributions': [147], 'this': [149], 'note;': [150], 'secondly': [152], 'triviality': [154], 'every': [156], 'assuming': [159], 'absence': [161], 'points.': [164]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2317890792', 'counts_by_year': [{'year': 2024, 'cited_by_count': 1}, {'year': 2023, 'cited_by_count': 1}, {'year': 2022, 'cited_by_count': 3}, {'year': 2021, 'cited_by_count': 1}, {'year': 2020, 'cited_by_count': 1}, {'year': 2017, 'cited_by_count': 1}, {'year': 2015, 'cited_by_count': 1}], 'updated_date': '2024-12-15T10:19:50.165239', 'created_date': '2016-06-24'}
Publication Information

Basic Information

Access and Citation

AI Researcher Chatbot

Primary Location

Authors

Topics

Keywords

Related Works
