대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제36권4호
  • /
  • Pages.783-800
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  • 2021
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  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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A NOTE ON GCR-LIGHTLIKE WARPED PRODUCT SUBMANIFOLDS IN INDEFINITE KAEHLER MANIFOLDS

  • Kumar, Sangeet (Department of Mathematics Sri Guru Teg Bahadur Khalsa College) ;
  • Pruthi, Megha (Department of Mathematics Sri Guru Teg Bahadur Khalsa College)
  • 투고 : 2020.08.13
  • 심사 : 2021.05.18
  • 발행 : 2021.10.31
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초록

We prove the non-existence of warped product GCR-lightlike submanifolds of the type K⊥ × λ KT such that KT is a holomorphic submanifold and K⊥ is a totally real submanifold in an indefinite Kaehler manifold $\tilde{K}$. Further, the existence of GCR-lightlike warped product submanifolds of the type KT × λ K⊥ is obtained by establishing a characterization theorem in terms of the shape operator and the warping function in an indefinite Kaehler manifold. Consequently, we find some necessary and sufficient conditions for an isometrically immersed GCR-lightlike submanifold in an indefinite Kaehler manifold to be a GCR-lightlike warped product, in terms of the canonical structures f and ω. Moreover, we also derive a geometric estimate for the second fundamental form of GCR-lightlike warped product submanifolds, in terms of the Hessian of the warping function λ.

키워드

과제정보

Sangeet Kumar wishes to thank Science and Engineering Research Board, GoI, New Delhi for the financial funding vide File No. ECR/2017/000786.

참고문헌

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