Geometric characterizations of almost Ricci-Bourguignon solitons on Kenmotsu manifolds

초록

The aim of this paper is to find the geometric characterizations of almost Ricci-Bourguignon solitons and gradient almost Ricci-Bourguignon solitons within the background of Kenmotsu manifolds. If (M, g) is a (2n+1)-dimensional Kenmotsu manifold and g represents an almost Ricci-Bourguignon soliton, then we find a sufficient condition under which the manifold M is Einstein (trivial). Next, we show that if g is an almost Ricci-Bourguignon soliton on M and the Reeb vector field 4 leaves lambda + pr invariant, then g reduces to Ricci-Bourguignon soliton on M. Finally, we prove that if g is a gradient almost Ricci-Bourguignon soliton, then the manifold M is either Einstein or g is a gradient n-Yamabe soliton on M. As a consequence of the results, we obtain several corollaries.

키워드