• Title/Summary/Keyword: Einstein space

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ON NON-PROPER PSEUDO-EINSTEIN RULED REAL HYPERSURFACES IN COMPLEX SPACE FORMS

  • Suh, Young-Jin
    • Bulletin of the Korean Mathematical Society
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    • v.36 no.2
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    • pp.315-336
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    • 1999
  • In the paper [12] we have introduced the new kind of pseudo-einstein ruled real hypersurfaces in complex space forms $M_n(c), c\neq0$, which are foliated by pseudo-Einstein leaves. The purpose of this paper is to give a geometric condition for non-proper pseudo-Einstein ruled real hypersurfaces to be totally geodesic in the sense of Kimura [8] for c> and Ahn, Lee and the present author [1] for c<0.

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EINSTEIN WARPED PRODUCT SPACES

  • KIM, DONG-SOO
    • Honam Mathematical Journal
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    • v.22 no.1
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    • pp.107-111
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    • 2000
  • We study Einstein warped product spaces. As a result, we prove the following: if M is an Einstein warped product space with base a compact 2-dimensional surface, then M is simply a Riemannian product space.

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p-BIHARMONIC HYPERSURFACES IN EINSTEIN SPACE AND CONFORMALLY FLAT SPACE

  • Ahmed Mohammed Cherif;Khadidja Mouffoki
    • Bulletin of the Korean Mathematical Society
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    • v.60 no.3
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    • pp.705-715
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    • 2023
  • In this paper, we present some new properties for p-biharmonic hypersurfaces in a Riemannian manifold. We also characterize the p-biharmonic submanifolds in an Einstein space. We construct a new example of proper p-biharmonic hypersurfaces. We present some open problems.

Super Quasi-Einstein Manifolds with Applications to General Relativity

  • Mallick, Sahanous
    • Kyungpook Mathematical Journal
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    • v.58 no.2
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    • pp.361-375
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    • 2018
  • The object of the present paper is to study super quasi-Einstein manifolds. Some geometric properties of super quasi-Einstein manifolds have been studied. We also discuss $S(QE)_4$ spacetime with space-matter tensor and some properties related to it. Finally, we construct an example of a super quasi-Einstein spacetime.

GENERALIZED m-QUASI-EINSTEIN STRUCTURE IN ALMOST KENMOTSU MANIFOLDS

  • Mohan Khatri;Jay Prakash Singh
    • Bulletin of the Korean Mathematical Society
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    • v.60 no.3
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    • pp.717-732
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    • 2023
  • The goal of this paper is to analyze the generalized m-quasi-Einstein structure in the context of almost Kenmotsu manifolds. Firstly we showed that a complete Kenmotsu manifold admitting a generalized m-quasi-Einstein structure (g, f, m, λ) is locally isometric to a hyperbolic space ℍ2n+1(-1) or a warped product ${\tilde{M}}{\times}{_{\gamma}{\mathbb{R}}$ under certain conditions. Next, we proved that a (κ, µ)'-almost Kenmotsu manifold with h' ≠ 0 admitting a closed generalized m-quasi-Einstein metric is locally isometric to some warped product spaces. Finally, a generalized m-quasi-Einstein metric (g, f, m, λ) in almost Kenmotsu 3-H-manifold is considered and proved that either it is locally isometric to the hyperbolic space ℍ3(-1) or the Riemannian product ℍ2(-4) × ℝ.

How the Geometries of Newton's Flat and Einstein's Curved Space-Time Explain the Laws of Motion

  • Yang, Kyoung-Eun
    • Journal for History of Mathematics
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    • v.32 no.1
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    • pp.17-25
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    • 2019
  • This essay elucidates the way the geometries of space-time theories explain material bodies' motions. A conventional attempt to interpret the way that space-time geometry explains is to consider the geometrical structure of space-time as involving a causally efficient entity that directs material bodies to follow their trajectories corresponding to the laws of motion. Newtonian substantival space is interpreted as an entity that acts but is not acted on by the motions of material bodies. And Einstein's curved space-time is interpreted as an entity that causes the motions of bodies. This essay argues against this line of thought and provides an alternative understanding of the way space-time geometry explain the laws of motion. The workings of the way that Newton's flat and Einstein's curved space-time explains the law of motion is such that space-time geometry encodes the principle of inertia which specifies straight lines of moving bodies.

STUDY OF P-CURVATURE TENSOR IN THE SPACE-TIME OF GENERAL RELATIVITY

  • Ganesh Prasad Pokhariyal;Sudhakar Kumar Chaubey
    • Honam Mathematical Journal
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    • v.45 no.2
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    • pp.316-324
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    • 2023
  • The P-curvature tensor has been studied in the space-time of general relativity and it is found that the contracted part of this tensor vanishes in the Einstein space. It is shown that Rainich conditions for the existence of non-null electro variance can be obtained by P𝛼𝛽. It is established that the divergence of tensor G𝛼𝛽 defined with the help of P𝛼𝛽 and scalar P is zero, so that it can be used to represent Einstein field equations. It is shown that for V4 satisfying Einstein like field equations, the tensor P𝛼𝛽 is conserved, if the energy momentum tensor is Codazzi type. The space-time satisfying Einstein's field equations with vanishing of P-curvature tensor have been considered and existence of Killing, conformal Killing vector fields and perfect fluid space-time has been established.

KAEHLER SUBMANIFOLDS WITH RS=0 IN A COMPLEX PROJECTIVE SPACE

  • Hyun, Jong-Ik
    • Communications of the Korean Mathematical Society
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    • v.12 no.3
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    • pp.685-690
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    • 1997
  • Our study focuses on the condition under which a subspace of complex projective space can become an Einstein space. We prove that a subspace becomes an Einstein space if it's codimension is less than n-1 and its curvature tensor and Ricci tensor satisfies Ryan's condition.

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SCREEN CONFORMAL EINSTEIN LIGHTLIKE HYPERSURFACES OF A LORENTZIAN SPACE FORM

  • Jin, Dae-Ho
    • Communications of the Korean Mathematical Society
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    • v.25 no.2
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    • pp.225-234
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    • 2010
  • In this paper, we study the geometry of lightlike hypersurfaces of a semi-Riemannian manifold. We prove a classification theorem for Einstein lightlike hypersurfaces M of a Lorentzian space form subject such that the second fundamental forms of M and its screen distribution S(TM) are conformally related by some non-vanishing smooth function.