• Title/Summary/Keyword: Riemannian manifolds

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EMBEDDING RIEMANNIAN MANIFOLDS VIA THEIR EIGENFUNCTIONS AND THEIR HEAT KERNEL

  • Abdalla, Hiba
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.5
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    • pp.939-947
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    • 2012
  • In this paper, we give a generalization of the embeddings of Riemannian manifolds via their heat kernel and via a finite number of eigenfunctions. More precisely, we embed a family of Riemannian manifolds endowed with a time-dependent metric analytic in time into a Hilbert space via a finite number of eigenfunctions of the corresponding Laplacian. If furthermore the volume form on the manifold is constant with time, then we can construct an embedding with a complete eigenfunctions basis.

SPACES OF CONFORMAL VECTOR FIELDS ON PSEUDO-RIEMANNIAN MANIFOLDS

  • KIM DONG-SOO;KIM YOUNG-HO
    • Journal of the Korean Mathematical Society
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    • v.42 no.3
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    • pp.471-484
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    • 2005
  • We study Riemannian or pseudo-Riemannian manifolds which carry the space of closed conformal vector fields of at least 2-dimension. Subject to the condition that at each point the set of closed conformal vector fields spans a non-degenerate subspace of the tangent space at the point, we prove a global and a local classification theorems for such manifolds.

RIEMANNIAN MANIFOLDS WITH A SEMI-SYMMETRIC METRIC P-CONNECTION

  • Chaubey, Sudhakar Kr;Lee, Jae Won;Yadav, Sunil Kr
    • Journal of the Korean Mathematical Society
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    • v.56 no.4
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    • pp.1113-1129
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    • 2019
  • We define a class of semi-symmetric metric connection on a Riemannian manifold for which the conformal, the projective, the concircular, the quasi conformal and the m-projective curvature tensors are invariant. We also study the properties of semisymmetric, Ricci semisymmetric and Eisenhart problems for solving second order parallel symmetric and skew-symmetric tensors on the Riemannian manifolds equipped with a semi-symmetric metric P-connection.

ISOSPECTRAL MANIFOLDS WITH DIFFERENT LOCAL GEOMETRY

  • Gordon, Carolyn S.
    • Journal of the Korean Mathematical Society
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    • v.38 no.5
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    • pp.955-970
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    • 2001
  • Two compact Riemannian manifolds are said to be isospectral if the associated Laplace-Beltrami operators have the same eigenvalue spectrum. We describe a method, based on the used of Riemannian submersions, for constructing isospectral manifolds with different local geometry and survey examples constructed through this method.

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CONFORMAL SEMI-SLANT SUBMERSIONS FROM LORENTZIAN PARA SASAKIAN MANIFOLDS

  • Kumar, Sushil;Prasad, Rajendra;Singh, Punit Kumar
    • Communications of the Korean Mathematical Society
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    • v.34 no.2
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    • pp.637-655
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    • 2019
  • In this paper, we introduce conformal semi-slant submersions from Lorentzian para Sasakian manifolds onto Riemannian manifolds. We investigate integrability of distributions and the geometry of leaves of such submersions from Lorentzian para Sasakian manifolds onto Riemannian manifolds. Moreover, we examine necessary and sufficient conditions for such submersions to be totally geodesic where characteristic vector field ${\xi}$ is vertical.

Critical rimennian metrics on cosymplectic manifolds

  • Kim, Byung-Hak
    • Journal of the Korean Mathematical Society
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    • v.32 no.3
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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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RIEMANNIAN SUBMANIFOLDS IN LORENTZIAN MANIFOLDS WITH THE SAME CONSTANT CURVATURES

  • Park, Joon-Sang
    • Bulletin of the Korean Mathematical Society
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    • v.39 no.2
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    • pp.237-249
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    • 2002
  • We study nondegenerate immersions of Riemannian manifolds of constant sectional curvatures into Lorentzian manifolds of the same constant sectional curvatures with flat normal bundles. We also give a method to produce such immersions using the so-called Grassmannian system. .