In present paper, after finding the conditions for the integrability of various distributions of a GCR-lightlike submanifold of indefinite Kenmotsu manifolds, we prove that there do not exist totally contact umbilical GCR-lightlike submanifolds of indefinite Kenmotsu manifolds other than totally contact geodesic GCR-lightlike submanifolds and moreover it is a totally geodesic GCR-lightlike submanifold.
📌 3 Key Takeaways
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Objective & Hypothesis:In present paper, after finding the conditions for the integrability of various distributions of a GCR-lightlike submanifold of indefinite Kenmotsu manifolds, we prove that there do not exist totally contact umbilical GCR-lightlike submanifolds of indefinite Kenmotsu manifolds other than totally contact geodesic GCR-lightlike submanifolds and moreover it is a totally geodesic GCR-lightlike submanifold.
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Key Findings & Data:In present paper, after finding the conditions for the integrability of various distributions of a GCR-lightlike submanifold of indefinite Kenmotsu manifolds, we prove that there do not exist totally contact umbilical GCR-lightlike submanifolds of indefinite Kenmotsu manifolds other than totally contact geodesic GCR-lightlike submanifolds and moreover it is a totally geodesic GCR-lightlike submanifold.
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Conclusion & Impact:In present paper, after finding the conditions for the integrability of various distributions of a GCR-lightlike submanifold of indefinite Kenmotsu manifolds, we prove that there do not exist totally contact umbilical GCR-lightlike submanifolds of indefinite Kenmotsu manifolds other than totally contact geodesic GCR-lightlike submanifolds and moreover it is a totally geodesic GCR-lightlike submanifold.
In present paper, after finding the conditions for the integrability of various distributions of a GCR-lightlike submanifold of indefinite Kenmotsu manifolds, we prove that there do not exist totally contact umbilical GCR-lightlike submanifolds of indefinite Kenmotsu manifolds other than totally contact geodesic GCR-lightlike submanifolds and moreover it is a totally geodesic GCR-lightlike submanifold.
KUMAR, R., NAGAICH, R. K., JAİN, V. (2022). Non existence of totally contact umbilical GCR-lightlike submanifolds of indefinite Kenmotsu manifolds. Hacettepe Journal of Mathematics and Statistics, Cilt: 44 - Sayı: 1, 83–91. https://ajindex.com/articles/528960