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Totally umbilical CR -submanifolds of Semi-Riemannian Kaehler manifolds

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  • K. L. Duggal
  • R. Sharma

Abstract

We study totally umbilical CR -submanifolds of a Kaehler manifold carrying a semi-Riemannian metric. It is shown that for dimension of the totally real distribution greater than one, these submanifolds are locally decomposable into a complex and a totally real submanifold of the Kaehler manifold. For dimension equal to one, we show, in particular, that they are endowed with a normal contact metric structure if and only if the second fundamental form is parallel.

Suggested Citation

  • K. L. Duggal & R. Sharma, 1987. "Totally umbilical CR -submanifolds of Semi-Riemannian Kaehler manifolds," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 10, pages 1-5, January.
    • Handle: RePEc:hin:jijmms:627876
    DOI: 10.1155/S0161171287000668
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