• 제목/요약/키워드: Einstein manifold

검색결과 175건 처리시간 0.023초

A CHARACTERIZATION THEOREM FOR LIGHTLIKE HYPERSURFACES OF SEMI-RIEMANNIAN MANIFOLDS OF QUASI-CONSTANT CURVATURES

  • Jin, Dae Ho
    • East Asian mathematical journal
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    • 제30권1호
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    • pp.15-22
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    • 2014
  • In this paper, we study lightlike hypersurfaces M of semi-Riemannian manifolds $\bar{M}$ of quasi-constant curvatures. Our main result is a characterization theorem for screen homothetic Einstein lightlike hypersurfaces of a Lorentzian manifold of quasi-constant curvature subject such that its curvature vector field ${\zeta}$ is tangent to M.

Conformally flat cosymplectic manifolds

  • Kim, Byung-Hak;Kim, In-Bae
    • 대한수학회논문집
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    • 제12권4호
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    • pp.999-1006
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    • 1997
  • We proved that if a fibred Riemannian space $\tilde{M}$ with cosymplectic structure is conformally flat, then $\tilde{M}$ is the locally product manifold of locally Euclidean spaces, that is locally Euclidean. Moreover, we investigated the fibred Riemannian space with cosymplectic structure when the Riemannian metric $\tilde{g}$ on $\tilde{M}$ is Einstein.

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RICCI AND SCALAR CURVATURES ON SU(3)

  • Kim, Hyun-Woong;Pyo, Yong-Soo;Shin, Hyun-Ju
    • 호남수학학술지
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    • 제34권2호
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    • pp.231-239
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    • 2012
  • In this paper, we obtain the Ricci curvature and the scalar curvature on SU(3) with some left invariant Riemannian metric. And then we get a necessary and sufficient condition for the scalar curvature (resp. the Ricci curvature) on the Riemannian manifold SU(3) to be positive.

TOTAL SCALAR CURVATURE AND EXISTENCE OF STABLE MINIMAL SURFACES

  • Hwang, Seung-Su
    • 호남수학학술지
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    • 제30권4호
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    • pp.677-683
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    • 2008
  • On a compact n-dimensional manifold M, it has been conjectured that a critical point metric of the total scalar curvature, restricted to the space of metrics with constant scalar curvature of volume 1, should be Einstein. The purpose of the present paper is to prove that a 3-dimensional manifold (M,g) is isometric to a standard sphere if ker $s^*_g{{\neq}}0$ and there is a lower Ricci curvature bound. We also study the structure of a compact oriented stable minimal surface in M.

A Class of Lorentzian α-Sasakian Manifolds

  • Yildiz, Ahmet;Turan, Mine;Murathan, Cengizhan
    • Kyungpook Mathematical Journal
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    • 제49권4호
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    • pp.789-799
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    • 2009
  • In this study we consider ${\varphi}$-conformally flat, ${\varphi}$-conharmonically flat, ${\varphi}$-projectively at and ${\varphi}$-concircularly flat Lorentzian ${\alpha}$-Sasakian manifolds. In all cases, we get the manifold will be an ${\eta}$-Einstein manifold.

SOME RESULTS ON PROJECTIVE CURVATURE TENSOR IN SASAKIAN MANIFOLDS

  • Gautam, Umesh Kumar;Haseeb, Abdul;Prasad, Rajendra
    • 대한수학회논문집
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    • 제34권3호
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    • pp.881-896
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    • 2019
  • In the present paper, we study certain curvature conditions satisfying by the projective curvature tensor in Sasakian manifolds with respect to the generalized-Tanaka-Webster connection. Finally, we give an example of a 3-dimensional Sasakian manifold with respect to the generalized-Tanaka-Webster connection.

SOME RECURRENT PROPERTIES OF LP-SASAKIAN NANIFOLDS

  • Venkatesha, Venkatesha;Somashekhara., P.
    • Korean Journal of Mathematics
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    • 제27권3호
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    • pp.793-801
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    • 2019
  • The aim of the present paper is to study certain recurrent properties of LP-Sasakian manifolds. Here we first describe Ricci ${\eta}$-recurrent LP-Sasakian manifolds. Further we study semi-generalized recurrent and three dimensional locally generalized concircularly ${\phi}$-recurrent LP-Sasakian manifolds and got interesting results.

SASAKIAN 3-MANIFOLDS ADMITTING A GRADIENT RICCI-YAMABE SOLITON

  • Dey, Dibakar
    • Korean Journal of Mathematics
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    • 제29권3호
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    • pp.547-554
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    • 2021
  • The object of the present paper is to characterize Sasakian 3-manifolds admitting a gradient Ricci-Yamabe soliton. It is shown that a Sasakian 3-manifold M with constant scalar curvature admitting a proper gradient Ricci-Yamabe soliton is Einstein and locally isometric to a unit sphere. Also, the potential vector field is an infinitesimal automorphism of the contact metric structure. In addition, if M is complete, then it is compact.