Abstract: In this paper we initiate the study of most general class of subman- ifolds of a Kaehler manifold which includes all existing classes of submanifolds (complex submanifolds, totally real submanifolds, CR-submanifolds, slant sub- manifolds). Such a submanifold M of a Kaehler manifold M has naturally defined operators �, F, and G (see Section 3 for the definition). First we study the basic properties of these operators for a general submanifold and latter we characterize submanifolds with paralleland show that essentially such submanifolds of a Kaehler manifold are CR-submanifold. We also give examples of submanifolds of a Kaehler manifold which have paralleland a submanifold on which the operatoris not parallel.
Publication Year: 2009
Publication Date: 2009-01-01
Language: en
Type: article
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