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arXiv · 1903.07387

On the geometry of lightlike submanifolds of indefinite statistical manifolds

Varun Jain·Amrinder Pal Singh·Rakesh Kumar
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Abstract

We study lightlike submanifolds of indefinite statistical manifolds. Contrary to the classical theory of submanifolds of statistical manifolds, lightlike submanifolds of indefinite statistical manifolds need not to be statistical submanifold. Therefore we obtain some conditions for a lightlike submanifold of indefinite statistical manifolds to be a lightlike statistical submanifold. We derive the expression of statistical sectional curvature and finally obtain some conditions for the induced statistical Ricci tensor on a lightlike submanifold of indefinite statistical manifolds to be symmetric.

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Varun Jain, Amrinder Pal Singh, Rakesh Kumar. 2019-03-18. On the geometry of lightlike submanifolds of indefinite statistical manifolds. https://doi.org/10.1142/s0219887820500991

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