Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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AN OPTIMAL INEQUALITY FOR WARPED PRODUCT LIGHTLIKE SUBMANIFOLDS

  • Kumar, Sangeet (Department of Mathematics, Sri Guru Teg Bahadur Khalsa College) ;
  • Pruthi, Megha (Department of Mathematics, Sri Guru Teg Bahadur Khalsa College)
  • Received : 2021.02.08
  • Accepted : 2021.05.12
  • Published : 2021.06.25
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Abstract

In this paper, we establish several geometric characterizations focusing on the relationship between the squared norm of the second fundamental form and the warping function of SCR-lightlike warped product submanifolds in an indefinite Kaehler manifold. In particular, we find an estimate for the squared norm of the second fundamental form h in terms of the Hessian of the warping function λ for SCR-lightlike warped product submanifolds of an indefinite complex space form. Consequently, we derive an optimal inequality, namely $${\parallel}h{\parallel}^2{\geq}2q\{{\Delta}(ln{\lambda})+{\parallel}{\nabla}(ln{\lambda}){\parallel}^2+\frac{c}{2}p\}$$, for SCR-lightlike warped product submanifolds in an indefinite complex space form. We also provide one non-trivial example for this class of warped products in an indefinite Kaehler manifold.

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References

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