Totally umbilical CR -submanifolds of Semi-Riemannian Kaehler manifolds

K. L. Duggal and R. Sharma

International Journal of Mathematics and Mathematical Sciences, 1987, vol. 10, 1-5

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.

Date: 1987
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:627876

DOI: 10.1155/S0161171287000668

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