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The main purpose of the paper is to prove that if a compact Riemannian manifold admits a gradient $\rho$-Einstein soliton such that the gradient Einstein potential is a non-trivial conformal vector field, then the manifold is isometric to the Euclidean sphere. We have showed that a Riemannian manifold satisfying gradient $\rho$-Einstein soliton with convex Einstein potential possesses non-negative scalar curvature. We have also deduced a sufficient condition for a Riemannian manifold to be compact which satisfies almost $\eta$-Ricci soliton.
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참고문헌 (19)
참고문헌 신청
W. Ambrose / 1957 / A theorem of Myers / Duke Math. J 24:345~348
C. Aquino / 2011 / Some Applications of the Hodge-de Rham Decomposition to Ricci Solitons / Results in Mathematics 60(1-4)
Abdênago Barros / 2013 / A note on rigidity of the almost Ricci soliton / Archiv der Mathematik 100(5):481~490
A. Barros / 2012 / Some characterizations for compact almost Ricci solitons / Proceedings of the American Mathematical Society 140(3):1033~1040
A. M. Blaga / 2018 / Almost-Ricci solitons in(LCS)n-manifolds / Bull. Belg. Math. Soc. Simon Stevin 25(5):641~653
Abdênago Barros / 2013 / A note on rigidity of the almost Ricci soliton / Archiv der Mathematik 100(5):481~490
A. Barros / 2012 / Some characterizations for compact almost Ricci solitons / Proceedings of the American Mathematical Society 140(3):1033~1040
A. M. Blaga / 2018 / Almost-Ricci solitons in(LCS)n-manifolds / Bull. Belg. Math. Soc. Simon Stevin 25(5):641~653
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