K. L. Duggal, R. Sharma, "Totally umbilical -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 -submanifolds of Semi-Riemannian Kaehler manifolds
We study totally umbilical -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.
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