International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1987 / Article

Open Access

Volume 10 |Article ID 627876 | https://doi.org/10.1155/S0161171287000668

K. L. Duggal, R. Sharma, "Totally umbilical CR-submanifolds of Semi-Riemannian Kaehler manifolds", International Journal of Mathematics and Mathematical Sciences, vol. 10, Article ID 627876, 5 pages, 1987. https://doi.org/10.1155/S0161171287000668

Totally umbilical CR-submanifolds of Semi-Riemannian Kaehler manifolds

Received18 Aug 1986
Revised20 Oct 1986

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.

Copyright © 1987 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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