Compact almost Ricci solitons with constant scalar curvature are gradient

By A. Barros, R. Batista, E. Ribeiro. 2012

98 citations recorded by the source corpus.

The aim of this note is to prove that any compact non-trivial almost Ricci soliton $$\big (M^n,\,g,\,X,\,\lambda \big )$$(Mn,g,X,λ) with constant scalar curvature is isometric to a Euclidean sphere $$\mathbb {S}^{n}$$Sn. As a consequence we obtain that every compact non-trivial almost Ricci soliton with constant scalar curvature is gradient. Moreover, the vector field $$X$$X decomposes as the sum of a Killing vector field $$Y$$Y and the gradient of a suitable function.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/68c252f6fd79672f914bd1d6937c57c79f3d9a85

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In Applied Mathematics

1. Ramesh Sharma
2. Amalendu Ghosh

In Astronomy and Astrophysics

1. Ramesh Sharma
2. Amalendu Ghosh

In Geometry and Topology

1. Ramesh Sharma
2. Amalendu Ghosh

Citations in the corpus

• Almost Ricci solitons and $$K$$K-contact geometry (2014, background): “For a simple example of an almost Ricci soliton with λ non-constant see [2].”