Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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CLASSIFICATION OF TWISTED PRODUCT LIGHTLIKE SUBMANIFOLDS

  • Sangeet Kumar (Department of Mathematics Sri Guru Teg Bahadur Khalsa College) ;
  • Megha Pruthi (Department of Mathematics Sri Guru Teg Bahadur Khalsa College)
  • Received : 2022.06.30
  • Accepted : 2023.02.10
  • Published : 2023.07.31
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Abstract

In this paper, we introduce the idea of twisted product lightlike submanifolds of semi-Riemannian manifolds and provide non-trivial examples of such lightlike submanifolds. Then, we prove the non-existence of proper isotropic or totally lightlike twisted product submanifolds of a semi-Riemannian manifold. We also show that for a twisted product lightlike submanifold of a semi-Riemannian manifold, the induced connection ∇ is not a metric connection. Further, we prove that a totally umbilical SCR-lightlike submanifold of an indefinite Kaehler manifold ${\tilde{M}}$ does not admit any twisted product SCR-lightlike submanifold of the type M⊥×ϕMT, where M⊥ is a totally real submanifold and MT is a holomorphic submanifold of ${\tilde{M}}$. Consequently, we obtain a geometric inequality for the second fundamental form of twisted product SCR-lightlike submanifolds of the type MT×ϕM⊥ of an indefinite Kaehler manifold ${\tilde{M}}$, in terms of the gradient of ln ϕ, where ϕ stands for the twisting function. Subsequently, the equality case of this inequality is discussed. Finally, we construct a non-trivial example of a twisted product SCR-lightlike submanifold in an indefinite Kaehler manifold.

Keywords

Acknowledgement

The authors would like to express their sincere gratitude to the referees for their valuable suggestions, which definitely improved the manuscript.

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