• 제목/요약/키워드: conharmonic curvature tensor

검색결과 9건 처리시간 0.018초

ON THE CONHARMONIC CURVATURE TENSOR OF A LOCALLY CONFORMAL ALMOST COSYMPLECTIC MANIFOLD

  • Abood, Habeeb M.;Al-Hussaini, Farah H.
    • 대한수학회논문집
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    • 제35권1호
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    • pp.269-278
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    • 2020
  • This paper aims to study the geometrical properties of the conharmonic curvature tensor of a locally conformal almost cosymplectic manifold. The necessary and sufficient conditions for the conharmonic curvature tensor to be flat, the locally conformal almost cosymplectic manifold to be normal and an η-Einstein manifold were determined.

Curvature Properties of 𝜂-Ricci Solitons on Para-Kenmotsu Manifolds

  • Singh, Abhishek;Kishor, Shyam
    • Kyungpook Mathematical Journal
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    • 제59권1호
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    • pp.149-161
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    • 2019
  • In the present paper, we study curvature properties of ${\eta}$-Ricci solitons on para-Kenmotsu manifolds. We obtain some results of ${\eta}$-Ricci solitons on para-Kenmotsu manifolds satisfying $R({\xi},X).C=0$, $R({\xi},X).{\tilde{M}}=0$, $R({\xi},X).P=0$, $R({\xi},X).{\tilde{C}}=0$ and $R({\xi},X).H=0$, where $C,\;{\tilde{M}},\;P,\;{\tilde{C}}$ and H are a quasi-conformal curvature tensor, a M-projective curvature tensor, a pseudo-projective curvature tensor, and a concircular curvature tensor and conharmonic curvature tensor, respectively.

A STUDY ON (k, 𝜇)'-ALMOST KENMOTSU MANIFOLDS

  • Li, Jin;Liu, Ximin;Ning, Wenfeng
    • 호남수학학술지
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    • 제40권2호
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    • pp.347-354
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    • 2018
  • Let ${\mathcal{C}}$, ${\mathcal{M}}$, ${\mathcal{L}}$ be concircular curvature tensor, M-projective curvature tensor and conharmonic curvature tensor, respectively. We obtain that if a non-Kenmotsu ($k,{\mu}$)'-almost Kenmotsu manifold satisfies ${\mathcal{C}}{\cdot}{\mathcal{S}}=0$, ${\mathcal{R}}{\cdot}{\mathcal{M}}=0$ or ${\mathcal{R}}{\cdot}{\mathcal{L}}=0$, then it is locally isometric to the Riemannian product ${\mathds{H}}^{n+1}(-4){\times}{\mathds{R}}^n$.

ON GENERALIZED QUASI-CONFORMAL N(k, μ)-MANIFOLDS

  • Baishya, Kanak Kanti;Chowdhury, Partha Roy
    • 대한수학회논문집
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    • 제31권1호
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    • pp.163-176
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    • 2016
  • The object of the present paper is to introduce a new curvature tensor, named generalized quasi-conformal curvature tensor which bridges conformal curvature tensor, concircular curvature tensor, projective curvature tensor and conharmonic curvature tensor. Flatness and symmetric properties of generalized quasi-conformal curvature tensor are studied in the frame of (k, ${\mu}$)-contact metric manifolds.

RICCI SOLITONS ON RICCI PSEUDOSYMMETRIC (LCS)n-MANIFOLDS

  • Hui, Shyamal Kumar;Lemence, Richard S.;Chakraborty, Debabrata
    • 호남수학학술지
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    • 제40권2호
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    • pp.325-346
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    • 2018
  • The object of the present paper is to study some types of Ricci pseudosymmetric $(LCS)_n$-manifolds whose metric is Ricci soliton. We found the conditions when Ricci soliton on concircular Ricci pseudosymmetric, projective Ricci pseudosymmetric, $W_3$-Ricci pseudosymmetric, conharmonic Ricci pseudosymmetric, conformal Ricci pseudosymmetric $(LCS)_n$-manifolds to be shrinking, steady and expanding. We also construct an example of concircular Ricci pseudosymmetric $(LCS)_3$-manifold whose metric is Ricci soliton.

TRANS-SASAKIAN MANIFOLDS WITH RESPECT TO GENERALIZED TANAKA-WEBSTER CONNECTION

  • Kazan, Ahmet;Karadag, H.Bayram
    • 호남수학학술지
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    • 제40권3호
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    • pp.487-508
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    • 2018
  • In this study, we use the generalized Tanaka-Webster connection on a trans-Sasakian manifold of type (${\alpha},{\beta}$) and obtain the curvature tensors of a trans-Sasakian manifold with respect to this connection. Also, we investigate some special curvature conditions of a trans-Sasakian manifold with respect to generalized Tanaka-Webster connection and finally, give an example for trans-Sasakian manifolds.

FIBRED RIEMANNIAN SPACE AND INFINITESIMAL TRANSFORMATION

  • Kim, Byung-Hak;Choi, Jin-Hyuk
    • Journal of applied mathematics & informatics
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    • 제24권1_2호
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    • pp.541-545
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    • 2007
  • In this paper, we study the infinitesimal transformation on the fibred Riemannian space. The conharmonic curvature tensor is invariant under the conharmonic transformation. We have proved that the conharmonically flat fibred Riemannian space with totally geodesic fibre is locally the Riemannian product of the base space and a fibre.