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Z Tensor on N(k)-Quasi-Einstein Manifolds

Uday Chand De|Sahanous Mallick
경북대학교 자연과학대학 수학과|2016.09|Kyungpook Mathematical Journal|제56권 제3호|pp. 979-991

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참고문헌

키워드

$k$-nullity distributionprojective curvature tensorquasi-Einstein manifoldsN(k)-quasi-Einstein manifolds$\mathcal{Z}$ tensorconformal curvature tensor.
주제분류수학

초록

The object of the present paper is to study N(k)-quasi-Einstein manifolds. We study an N(k)-quasi-Einstein manifold satisfying the curvature conditions $R(\xi ,X)\cdot \mathcal{Z}=0$,$\mathcal{Z}(X,\xi )\cdot R=0$, and $P(\xi ,X)\cdot \mathcal{Z}=0$, where $R$, $P$ and $\mathcal{Z}$ denote the Riemannian curvature tensor,the projective curvature tensor and $\mathcal{Z}$ tensor respectively. Next we prove that the curvature condition$C\cdot \mathcal{Z}=0$ holds in an N(k)-quasi-Einstein manifold, where $C$ is the conformal curvature tensor. We also study $\mathcal{Z}$-recurrent N(k)-quasi-Einstein manifolds. Finally, we construct an example of an N(k)-quasi-Einsteinmanifold and mention some physical examples.

Abstract

The object of the present paper is to study N(k)-quasi-Einstein manifolds. We study an N(k)-quasi-Einstein manifold satisfying the curvature conditions $R(\xi ,X)\cdot \mathcal{Z}=0$,$\mathcal{Z}(X,\xi )\cdot R=0$, and $P(\xi ,X)\cdot \mathcal{Z}=0$, where $R$, $P$ and $\mathcal{Z}$ denote the Riemannian curvature tensor,the projective curvature tensor and $\mathcal{Z}$ tensor respectively. Next we prove that the curvature condition$C\cdot \mathcal{Z}=0$ holds in an N(k)-quasi-Einstein manifold, where $C$ is the conformal curvature tensor. We also study $\mathcal{Z}$-recurrent N(k)-quasi-Einstein manifolds. Finally, we construct an example of an N(k)-quasi-Einsteinmanifold and mention some physical examples.

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관련 논문AI추천

QUASI-CONFORMAL CURVATURE TENSOR ON N (k)-QUASI EINSTEIN MANIFOLDSAvijit Sarkar, Dipankar Hazra강원경기수학회 · 한국수학논문집2021 · 제29권 제4호ON CONFORMAL AND QUASI-CONFORMAL CURVATURE TENSORS OF AN N(k)-QUASI EINSTEIN MANIFOLDAbolfazl Taleshian, Aliakbar Hosseinzadeh대한수학회 · 대한수학회논문집2012 · 제27권 제2호On a class of N(k)-quasi einstein manifoldsAbul Kalam Gazi, Avik De, Uday Chand De대한수학회 · 대한수학회논문집2011 · 제26권 제4호ON GENERALIZED Z-RECURRENT MANIFOLDSPrajjwal Pal, Uday Chand De한국수학교육학회 · 이론수학과 교직수학2017 · 제24권 제2호On some classes of generalized quasi-Einstein manifoldsAbsos Ali Shaikh, Shyamal Kumar Hui대한수학회 · 대한수학회논문집2009 · 제24권 제3호On quasi Einstein manifoldsBiman Kanti De, Uday Chand De대한수학회 · 대한수학회논문집2008 · 제23권 제3호

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