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On contact CR-submanifolds of sasakian manifolds

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  • Koji Matsumoto

Abstract

Recently, K.Yano and M.Kon [5] have introduced the notion of a contact C R -submanifold of a Sasakian manifold which is closely similar to the one of a C R -submanifold of a Kaehlerian manifold defined by A. Bejancu [1]. In this paper, we shall obtain some fundamental properties of contact C R -submanifolds of a Sasakian manifold. Next, we shall calculate the length of the second fundamental form of a contact C R -product of a Sasakian space form (THEOREM 7.4). At last, we shall prove that a totally umbilical contact C R -submanifold satisfying certain conditions is totally geodesic in the ambient manifold (THEOREM 8.1).

Suggested Citation

  • Koji Matsumoto, 1983. "On contact CR-submanifolds of sasakian manifolds," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 6, pages 1-14, January.
    • Handle: RePEc:hin:jijmms:304272
    DOI: 10.1155/S0161171283000277
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