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Ricci almost solitons and contact geometry
Advances in Geometry ( IF 0.5 ) Pub Date : 2021-04-01 , DOI: 10.1515/advgeom-2019-0026
Amalendu Ghosh 1
Affiliation  

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.

中文翻译:

里奇几乎孤子和接触几何

我们证明,在K接触流形上,当且仅当势矢量场V是沿Reeb矢量场ξ的Jacobi场时,Ricci孤子才是Ricci孤子。然后,我们将接触度量作为具有平行Ricci张量的Ricci几乎孤子研究。为此,我们考虑了Ricci几乎是孤子,其潜在矢量场是接触矢量场,并证明了一些刚性结果。
更新日期:2021-04-16
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