• 제목/요약/키워드: Ricci-recurrent

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ON GENERALIZED RICCI-RECURRENT TRANS-SASAKIAN MANIFOLDS

  • Kim, Jeong-Sik;Prasad, Rajendra;Tripathi, Mukut-Mani
    • 대한수학회지
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    • 제39권6호
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    • pp.953-961
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    • 2002
  • Generalized Ricci-recurrent trans-Sasakian manifolds are studied. Among others, it is proved that a generalized Ricci-recurrent cosymplectic manifold is always recurrent Generalized Ricci-recurrent trans-Sasakian manifolds of dimension $\geq$ 5 are locally classified. It is also proved that if M is one of Sasakian, $\alpha$-Sasakian, Kenmotsu or $\beta$-Kenmotsu manifolds, which is gener-alized Ricci-recurrent with cyclic Ricci tensor and non-zero A (ξ) everywhere; then M is an Einstein manifold.

ON THE EXISTENCE OF SOME TYPES OF LP-SASAKIAN MANIFOLDS

  • Shaikh, Absos A.;Baishya, Kanak K.;Eyasmin, Sabina
    • 대한수학회논문집
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    • 제23권1호
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    • pp.95-110
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    • 2008
  • The object of the present paper is to provide the existence of LP-Sasakian manifolds with $\eta$-recurrent, $\eta$-parallel, $\phi$-recurrent, $\phi$-parallel Ricci tensor with several non-trivial examples. Also generalized Ricci recurrent LP-Sasakian manifolds are studied with the existence of various examples.

SOME NOTES ON NEARLY COSYMPLECTIC MANIFOLDS

  • Yildirim, Mustafa;Beyendi, Selahattin
    • 호남수학학술지
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    • 제43권3호
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    • pp.539-545
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    • 2021
  • In this paper, we study some symmetric and recurrent conditions of nearly cosymplectic manifolds. We prove that Ricci-semisymmetric and Ricci-recurrent nearly cosymplectic manifolds are Einstein and conformal flat nearly cosymplectic manifold is locally isometric to Riemannian product ℝ × N, where N is a nearly Kähler manifold.

ON QUASI RICCI SYMMETRIC MANIFOLDS

  • Kim, Jaeman
    • Korean Journal of Mathematics
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    • 제27권1호
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    • pp.9-15
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    • 2019
  • In this paper, we study a type of Riemannian manifold, namely quasi Ricci symmetric manifold. Among others, we show that the scalar curvature of a quasi Ricci symmetric manifold is constant. In addition if the manifold is Einstein, then its Ricci tensor is zero. Also we prove that if the associated vector field of a quasi Ricci symmetric manifold is either recurrent or concurrent, then its Ricci tensor is zero.

On Quasi-Conformally Recurrent Manifolds with Harmonic Quasi-Conformal Curvature Tensor

  • Shaikh, Absos Ali;Roy, Indranil
    • Kyungpook Mathematical Journal
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    • 제51권1호
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    • pp.109-124
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    • 2011
  • The main objective of the paper is to provide a full classification of quasi-conformally recurrent Riemannian manifolds with harmonic quasi-conformal curvature tensor. Among others it is shown that a quasi-conformally recurrent manifold with harmonic quasi-conformal curvature tensor is any one of the following: (i) quasi-conformally symmetric, (ii) conformally flat, (iii) manifold of constant curvature, (iv) vanishing scalar curvature, (v) Ricci recurrent.

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.

On Generalized Ricci Recurrent Spacetimes

  • Dey, Chiranjib
    • Kyungpook Mathematical Journal
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    • 제60권3호
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    • pp.571-584
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    • 2020
  • The object of the present paper is to characterize generalized Ricci recurrent (GR4) spacetimes. Among others things, it is proved that a conformally flat GR4 spacetime is a perfect fluid spacetime. We also prove that a GR4 spacetime with a Codazzi type Ricci tensor is a generalized Robertson Walker spacetime with Einstein fiber. We further show that in a GR4 spacetime with constant scalar curvature the energy momentum tensor is semisymmetric. Further, we obtain several corollaries. Finally, we cite some examples which are sufficient to demonstrate that the GR4 spacetime is non-empty and a GR4 spacetime is not a trivial case.

On Generalized 𝜙-recurrent Kenmotsu Manifolds with respect to Quarter-symmetric Metric Connection

  • Hui, Shyamal Kumar;Lemence, Richard Santiago
    • Kyungpook Mathematical Journal
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    • 제58권2호
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    • pp.347-359
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    • 2018
  • A Kenmotsu manifold $M^n({\phi},\;{\xi},\;{\eta},\;g)$, (n = 2m + 1 > 3) is called a generalized ${\phi}-recurrent$ if its curvature tensor R satisfies $${\phi}^2(({\nabla}_wR)(X,Y)Z)=A(W)R(X,Y)Z+B(W)G(X,Y)Z$$ for all $X,\;Y,\;Z,\;W{\in}{\chi}(M)$, where ${\nabla}$ denotes the operator of covariant differentiation with respect to the metric g, i.e. ${\nabla}$ is the Riemannian connection, A, B are non-vanishing 1-forms and G is given by G(X, Y)Z = g(Y, Z)X - g(X, Z)Y. In particular, if A = 0 = B then the manifold is called a ${\phi}-symmetric$. Now, a Kenmotsu manifold $M^n({\phi},\;{\xi},\;{\eta},\;g)$, (n = 2m + 1 > 3) is said to be generalized ${\phi}-Ricci$ recurrent if it satisfies $${\phi}^2(({\nabla}_wQ)(Y))=A(X)QY+B(X)Y$$ for any vector field $X,\;Y{\in}{\chi}(M)$, where Q is the Ricci operator, i.e., g(QX, Y) = S(X, Y) for all X, Y. In this paper, we study generalized ${\phi}-recurrent$ and generalized ${\phi}-Ricci$ recurrent Kenmotsu manifolds with respect to quarter-symmetric metric connection and obtain a necessary and sufficient condition of a generalized ${\phi}-recurrent$ Kenmotsu manifold with respect to quarter symmetric metric connection to be generalized Ricci recurrent Kenmotsu manifold with respect to quarter symmetric metric connection.

CERTAIN RESULTS ON CONTACT METRIC GENERALIZED (κ, µ)-SPACE FORMS

  • Huchchappa, Aruna Kumara;Naik, Devaraja Mallesha;Venkatesha, Venkatesha
    • 대한수학회논문집
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    • 제34권4호
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    • pp.1315-1328
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    • 2019
  • The object of the present paper is to study ${\eta}$-recurrent ${\ast}$-Ricci tensor, ${\ast}$-Ricci semisymmetric and globally ${\varphi}-{\ast}$-Ricci symmetric contact metric generalized (${\kappa}$, ${\mu}$)-space form. Besides these, ${\ast}$-Ricci soliton and gradient ${\ast}$-Ricci soliton in contact metric generalized (${\kappa}$, ${\mu}$)-space form have been studied.