• Title/Summary/Keyword: Einstein space

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The 𝒲-curvature Tensor on Relativistic Space-times

  • Abu-Donia, Hassan;Shenawy, Sameh;Syied, Abdallah Abdelhameed
    • Kyungpook Mathematical Journal
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    • v.60 no.1
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    • pp.185-195
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    • 2020
  • This paper aims to study the 𝒲-curvature tensor on relativistic space-times. The energy-momentum tensor T of a space-time having a semi-symmetric 𝒲-curvature tensor is semi-symmetric, whereas the whereas the energy-momentum tensor T of a space-time having a divergence free 𝒲-curvature tensor is of Codazzi type. A space-time having a traceless 𝒲-curvature tensor is Einstein. A 𝒲-curvature flat space-time is Einstein. Perfect fluid space-times which admits 𝒲-curvature tensor are considered.

ON WARPED PRODUCT SPACES WITH A CERTAIN RICCI CONDITION

  • Kim, Byung Hak;Lee, Sang Deok;Choi, Jin Hyuk;Lee, Young Ok
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.5
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    • pp.1683-1691
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    • 2013
  • In this paper, we obtain the criteria that the Riemannian manifold B is Einstein or a gradient Ricci soliton from the information of the second derivative of $f$ in the warped product space $R{\times}_fB$ with gradient Ricci solitons. Moreover, we construct new examples of non-Einstein gradient Ricci soliton spaces with an Einstein or non-Einstein gradient Ricci soliton leaf using our main theorems. Finally we also get analogous criteria for the Lorentzian version.

ON A TOTALLY UMBILIC HYPERSURFACE OF FIRST ORDER

  • Kim, Jaeman
    • Honam Mathematical Journal
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    • v.39 no.4
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    • pp.465-473
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    • 2017
  • In this paper, we define a totally umbilic hypersurface of first order and show that a totally umbilic hypersurface of first order in an Einstein manifold has a parallel second fundamental form. Furthermore we prove that a complete, simply connected and totally umbilic hypersurface of first order in a space of constant curvature is a Riemannian product of Einstein manifolds. Finally we show a proper example which is a totally umbilic hypersurface of first order but not a totally umbilic hypersurface.

EINSTEIN HALF LIGHTLIKE SUBMANIFOLDS WITH SPECIAL CONFORMALITIES

  • Jin, Dae Ho
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.6
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    • pp.1163-1178
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    • 2012
  • In this paper, we study the geometry of Einstein half lightlike submanifolds M of a semi-Riemannian space form $\bar{M}(c)$ subject to the conditions: (a) M is screen conformal, and (b) the coscreen distribution of M is a conformal Killing one. The main result is a classification theorem for screen conformal Einstein half lightlike submanifolds of a Lorentzian space form with a conformal Killing coscreen distribution.

EINSTEIN LIGHTLIKE HYPERSURFACES OF A LORENTZ SPACE FORM WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION

  • Jin, Dae Ho
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.4
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    • pp.1367-1376
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    • 2013
  • We study Einstein lightlike hypersurfaces M of a Lorentzian space form $\tilde{M}(c)$ admitting a semi-symmetric non-metric connection subject to the conditions; (1) M is screen conformal and (2) the structure vector field ${\zeta}$ of $\tilde{M}$ belongs to the screen distribution S(TM). The main result is a characterization theorem for such a lightlike hypersurface.

EINSTEIN LIGHTLIKE HYPERSURFACES OF A LORENTZIAN SPACE FORM WITH A SEMI-SYMMETRIC METRIC CONNECTION

  • Jin, Dae Ho
    • Communications of the Korean Mathematical Society
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    • v.28 no.1
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    • pp.163-175
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    • 2013
  • In this paper, we prove a classification theorem for Einstein lightlike hypersurfaces M of a Lorentzian space form ($\bar{M}$(c), $\bar{g}$) with a semi-symmetric metric connection subject such that the second fundamental forms of M and its screen distribution S(TM) are conformally related by some non-zero constant.

EINSTEIN SPACES AND CONFORMAL VECTOR FIELDS

  • KIM DONG-SOO;KIM YOUNG HO;PARK SEONG-HEE
    • Journal of the Korean Mathematical Society
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    • v.43 no.1
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    • pp.133-145
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    • 2006
  • We study Riemannian or pseudo-Riemannian manifolds which admit a closed conformal vector field. Subject to the condition that at each point $p{\in}M^n$ the set of conformal gradient vector fields spans a non-degenerate subspace of TpM, using a warped product structure theorem we give a complete description of the space of conformal vector fields on arbitrary non-Ricci flat Einstein spaces.

Conformally Flat Quasi-Einstein Spaces

  • Chand De, Uday;Sengupta, Joydeep;Saha, Diptiman
    • Kyungpook Mathematical Journal
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    • v.46 no.3
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    • pp.417-423
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    • 2006
  • The object of the present paper is to study a conformally flat quasi-Einstein space and its hypersurface.

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