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On Generic submanifolds of a locally conformal Kahler manifold with parallel canonical structures

Author

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  • M. Hasan shahid
  • A. Sharfuddin

Abstract

The study of CR -submanifolds of a Kähler manifold was initiated by Bejancu [1]. Since then many papers have appeared on CR -submanifolds of a Kähler manifold. Also, it has been studied that generic submanifolds of Kähler manifolds [2] are generalisations of holomorphic submanifolds, totally real submanifolds and CR -submanifolds of Kähler manifolds. On the other hand, many examples C 2 of generic surfaces in which are not CR -submanifolds have been given by Chen [3] and this leads to the present paper where we obtain some necessary conditions for a generic submanifolds in a locally conformal Kähler manifold with four canonical strucrures, denoted by P , F , t and f , to have parallel P , F and t . We also prove that for a generic submanifold of a locally conformal Kähler manifold, F is parallel iff t is parallel.

Suggested Citation

  • M. Hasan shahid & A. Sharfuddin, 1995. "On Generic submanifolds of a locally conformal Kahler manifold with parallel canonical structures," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 18, pages 1-10, January.
    • Handle: RePEc:hin:jijmms:361574
    DOI: 10.1155/S0161171295000421
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