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Journal of Geometry

, 109:21 | Cite as

Geometry of warped product lightlike submanifolds of indefinite nearly Kaehler manifolds

  • Sangeet Kumar
Article

Abstract

The aim of present paper is to study geometry of warped product SCR-lightlike submanifolds of indefinite nearly Kaehler manifolds. We prove the non-existence of warped product SCR-lightlike submanifolds of the type \(N_{\bot } \times _{f} N_{T}\) in an indefinite nearly Kaehler manifold. We find a necessary and sufficient condition for a SCR-lightlike submanifold of an indefinite nearly Kaehler manifold to be a SCR-lightlike warped product submanifold of the type \(N_{T} \times _{f} N_{\bot }\). We give some characterizations in terms of the canonical structures T and \(\omega \) on a SCR-lightlike submanifold of an indefinite nearly Kaehler manifold under which it reduces to a SCR-lightlike warped product submanifold. We also prove that for a proper SCR-lightlike warped product submanifold of an indefinite nearly Kaehler manifold, the induced connection \(\nabla \) can never be a metric connection. Finally, we obtain a sharp inequality for the squared norm of the second fundamental form in terms of the warping function for a SCR-lightlike warped product submanifold of an indefinite nearly Kaehler manifold.

Keywords

Indefinite nearly Kaehler manifolds Warped product lightlike submanifolds SCR-lightlike submanifolds Totally umbilical lightlike submanifolds 

Mathematics Subject Classification

Primary 53C50 Secondary 53C15, 53C40, 53C55 

Notes

Acknowledgements

Sangeet Kumar is grateful to SERB-DST, New Delhi for the financial funding vide File No. ECR/2017/000786.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsSGTB Khalsa CollegeSri Anandpur Sahib, Distt.-RupnagarIndia

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