Some characterizations of $\rho $-Einstein solitons on Sasakian manifolds

Patra, Dhriti Sundar 

Canadian mathematical bulletin, Tome 65 (2022) no. 4, pp. 1036-1049

Résumé

The $\rho $-Einstein soliton is a self-similar solution of the Ricci–Bourguignon flow, which includes or relates to some famous geometric solitons, for example, the Ricci soliton and the Yamabe soliton, and so on. This paper deals with the study of $\rho $-Einstein solitons on Sasakian manifolds. First, we prove that if a Sasakian manifold M admits a nontrivial$\rho $-Einstein soliton $(M,g,V,\lambda )$, then M is $\mathcal {D}$-homothetically fixed null $\eta $-Einstein and the soliton vector field V is Jacobi field along trajectories of the Reeb vector field $\xi $, nonstrict infinitesimal contact transformation and leaves $\varphi $ invariant. Next, we find two sufficient conditions for a compact $\rho $-Einstein almost soliton to be trivial (Einstein) under the assumption that the soliton vector field is an infinitesimal contact transformation or is parallel to the Reeb vector field $\xi $.

Détail

DOI : 10.4153/S0008439522000078

Mots-clés : ρ-Einstein soliton, Sasakian manifold, null η-Einstein manifold, infinitesimal contact transformation, infinitesimal automorphism