• 제목/요약/키워드: product manifold

검색결과 137건 처리시간 0.03초

CR-WARPED PRODUCT SUBMANIFOLDS OF NEARLY KAEHLER MANIFOLDS

  • Al-Luhaibi, Nadia S.;Al-Solamy, Falleh R.;Khan, Viqar Azam
    • 대한수학회지
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    • 제46권5호
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    • pp.979-995
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    • 2009
  • As warped product manifolds provide an excellent setting to model space time near black holes or bodies with large gravitational field, the study of these manifolds assumes significance in general. B. Y. Chen [4] initiated the study of CR-warped product submanifolds in a Kaehler manifold. He obtained a characterization for a CR-submanifold to be locally a CR-warped product and an estimate for the squared norm of the second fundamental form of CR-warped products in a complex space form (cf [6]). In the present paper, we have obtained a necessary and sufficient conditions in terms of the canonical structures P and F on a CR-submanifold of a nearly Kaehler manifold under which the submanifold reduces to a locally CR-warped product submanifold. Moreover, an estimate for the second fundamental form of the submanifold in a generalized complex space is obtained and thus extend the results of Chen to a more general setting.

A NOTE ON GCR-LIGHTLIKE WARPED PRODUCT SUBMANIFOLDS IN INDEFINITE KAEHLER MANIFOLDS

  • Kumar, Sangeet;Pruthi, Megha
    • 대한수학회논문집
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    • 제36권4호
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    • pp.783-800
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    • 2021
  • 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.

Critical rimennian metrics on cosymplectic manifolds

  • Kim, Byung-Hak
    • 대한수학회지
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    • 제32권3호
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    • pp.553-562
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    • 1995
  • In a Recent paper [3], D. Chinea, M. Delon and J. C. Marrero proved that a cosymplectic manifold is formal and constructed an example of compact cosymplectic manifold which is not a global product of a Kaehler manifold with the circle. In this paper we study the compact cosymplectic manifolds with critical Riemannian metrics.

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A NEW TYPE WARPED PRODUCT METRIC IN CONTACT GEOMETRY

  • Mollaogullari, Ahmet;Camci, Cetin
    • 호남수학학술지
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    • 제44권1호
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    • pp.62-77
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    • 2022
  • This study presents an 𝛼-Sasakian structure on the product manifold M1 × 𝛽(I), where M1 is a Kähler manifold with an exact 1-form, and 𝛽(I) is an open curve. It then defines a new type warped product metric to study the warped product of almost Hermitian manifolds with almost contact metric manifolds, contact metric manifolds, and K-contact manifolds.

ON ALMOST QUASI RICCI SYMMETRIC MANIFOLDS

  • Kim, Jaeman
    • 대한수학회논문집
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    • 제35권2호
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    • pp.603-611
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    • 2020
  • The purpose of this note is to introduce a type of Riemannian manifold called an almost quasi Ricci symmetric manifold and investigate the several properties of such a manifold on which some geometric conditions are imposed. And the existence of such a manifold is ensured by a proper example.

On f-cosymplectic and (k, µ)-cosymplectic Manifolds Admitting Fischer -Marsden Conjecture

  • Sangeetha Mahadevappa;Halammanavar Gangadharappa Nagaraja
    • Kyungpook Mathematical Journal
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    • 제63권3호
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    • pp.507-519
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    • 2023
  • The aim of this paper is to study the Fisher-Marsden conjucture in the frame work of f-cosymplectic and (k, µ)-cosymplectic manifolds. First we prove that a compact f-cosymplectic manifold satisfying the Fisher-Marsden equation R'*g = 0 is either Einstein manifold or locally product of Kahler manifold and an interval or unit circle S1. Further we obtain that in almost (k, µ)-cosymplectic manifold with k < 0, the Fisher-Marsden equation has a trivial solution.

ON THE RICCI CURVATURE OF SUBMANIFOLDS IN THE WARPED PRODUCT L × f F

  • Kim, Young-Mi;Pak, Jin-Suk
    • 대한수학회지
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    • 제39권5호
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    • pp.693-708
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    • 2002
  • The warped product L$\times$$_{f}$ F of a line L and a Kaehler manifold F is a typical example of Kenmotsu manifold. In this paper we determine submanifolds of L$\times$$_{f}$ F which are tangent to the structure vector field and satisfy certain conditions concerning with Ricci curvature and mean curvature.ure.

PRODUCT OF PL FIBRATORS AS CODIMENSION-k FIBRATORS

  • Im, Young-Ho;Kim, Yong-Kuk
    • 대한수학회논문집
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    • 제22권2호
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    • pp.289-295
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    • 2007
  • We describe some conditions under which the product of two groups with certain property is a group with the same property, and we describe some conditions under which the product of hopfian manifolds is another hopfian manifold. As applications, we find some PL fibrators among the product of fibrators.