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Advances in Geometry

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Ricci almost solitons and contact geometry

Amalendu Ghosh
  • Corresponding author
  • Department of Mathematics, Chandernagore College, Chandannagar, Hooghly: 712 136, West Bengal, India
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Published Online: 2019-09-11 | DOI: https://doi.org/10.1515/advgeom-2019-0026


We prove that on a K-contact manifold, a Ricci almost soliton is a Ricci soliton if and only if the potential vector field V is a Jacobi field along the Reeb vector field ξ. Then we study contact metric as a Ricci almost soliton with parallel Ricci tensor. To this end, we consider Ricci almost solitons whose potential vector field is a contact vector field and prove some rigidity results.

Keywords: Contact metric manifold; K-contact manifold; contact vector field; Ricci almost soliton; Jacobi field

MSC 2010: 53C24; 53C15; 53C21


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About the article

Received: 2018-04-19

Revised: 2018-07-24

Revised: 2019-06-17

Published Online: 2019-09-11

Communicated by: P. Eberlein

Citation Information: Advances in Geometry, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2019-0026.

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