• Title, Summary, Keyword: locally symmetric

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TWO CHARACTERIZATION THEOREMS FOR HALF LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE KENMOTSU MANIFOLD

  • Jin, Dae Ho
    • The Pure and Applied Mathematics
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    • v.21 no.1
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    • pp.1-10
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    • 2014
  • In this paper, we study the curvature of locally symmetric or semi-symmetric half lightlike submanifolds M of an indefinite Kenmotsu manifold $\bar{M}$, whose structure vector field is tangent to M. After that, we study the existence of the totally geodesic screen distribution of half lightlike submanifolds of indefinite Kenmotsu manifolds with parallel co-screen distribution subject to the conditions: (1) M is locally symmetric, or (2) the lightlike transversal connection is flat.

LINEAR WEINGARTEN SPACELIKE HYPERSURFACES IN LOCALLY SYMMETRIC LORENTZ SPACE

  • Yang, Dan
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.2
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    • pp.271-284
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    • 2012
  • Let M be a linear Weingarten spacelike hypersurface in a locally symmetric Lorentz space with R = aH + b, where R and H are the normalized scalar curvature and the mean curvature, respectively. In this paper, we give some conditions for the complete hypersurface M to be totally umbilical.

LOCALLY SYMMETRIC HALF LIGHTLIKE SUBMANIFOLDS IN AN INDEFINITE KENMOTSU MANIFOLD

  • Jin, Dae-Ho
    • Communications of the Korean Mathematical Society
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    • v.27 no.3
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    • pp.583-589
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    • 2012
  • In this paper, we study locally symmetric half lightlike submanifolds M of an indefinite Kenmotsu manifold $\bar{M}$ subject to the conditions: (1) The transversal vector bundle $tr(TM)$ is parallel with respect to the connection $\bar{\nabla}$ of $\bar{M}$ and (2) M is irrotational.

LOCALLY SYMMETRIC ALMOST COKÄHLER 5-MANIFOLDS WITH KÄHLERIAN LEAVES

  • Wang, Yaning
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.3
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    • pp.789-798
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    • 2018
  • Let M be a compact almost $coK{\ddot{a}}hler$ 5-manifold with $K{\ddot{a}}hlerian$ leaves. In this paper, we prove that M is locally symmetric if and only if it is locally isometric to a Riemannian product of a unit circle $S^1$ and a locally symmetric compact $K{\ddot{a}}hler$ 4-manifold.

EQUIVALENCE CONDITIONS OF SYMMETRY PROPERTIES IN LIGHTLIKE HYPERSURFACES OF INDEFINITE KENMOTSU MANIFOLDS

  • Lungiambudila, Oscar;Massamba, Fortune;Tossa, Joel
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.4
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    • pp.1259-1280
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    • 2016
  • The paper deals with lightlike hypersurfaces which are locally symmetric, semi-symmetric and Ricci semi-symmetric in indefinite Kenmotsu manifold having constant $\bar{\phi}$-holomorphic sectional curvature c. We obtain that these hypersurfaces are totally goedesic under certain conditions. The non-existence condition of locally symmetric lightlike hyper-surfaces are given. Some Theorems of specific lightlike hypersurfaces are established. We prove, under a certain condition, that in lightlike hyper-surfaces of an indefinite Kenmotsu space form, tangent to the structure vector field, the parallel, semi-parallel, local symmetry, semi-symmetry and Ricci semi-symmetry notions are equivalent.

ON LOCALLY 𝜙-CONFORMALLY SYMMETRIC ALMOST KENMOTSU MANIFOLDS WITH NULLITY DISTRIBUTIONS

  • De, Uday Chand;Mandal, Krishanu
    • Communications of the Korean Mathematical Society
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    • v.32 no.2
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    • pp.401-416
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    • 2017
  • The aim of this paper is to investigate locally ${\phi}-conformally$ symmetric almost Kenmotsu manifolds with its characteristic vector field ${\xi}$ belonging to some nullity distributions. Also, we give an example of a 5-dimensional almost Kenmotsu manifold such that ${\xi}$ belongs to the $(k,\;{\mu})^{\prime}$-nullity distribution and $h^{\prime}{\neq}0$.

A MAXIMUM PRINCIPLE FOR COMPLETE HYPERSURFACES IN LOCALLY SYMMETRIC RIEMANNIAN MANIFOLD

  • Zhang, Shicheng
    • Communications of the Korean Mathematical Society
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    • v.29 no.1
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    • pp.141-153
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    • 2014
  • In this article, we apply the weak maximum principle in order to obtain a suitable characterization of the complete linearWeingarten hypersurfaces immersed in locally symmetric Riemannian manifold $N^{n+1}$. Under the assumption that the mean curvature attains its maximum and supposing an appropriated restriction on the norm of the traceless part of the second fundamental form, we prove that such a hypersurface must be either totally umbilical or hypersurface is an isoparametric hypersurface with two distinct principal curvatures one of which is simple.