Geometry of almost contact metrics as an almost *-?-Ricci-Bourguignon solitons

초록

In this paper, we give some characterizations by considering almost *-?-Ricci-Bourguignon soliton as a Kenmotsu metric. It is shown that if a Kenmotsu metric endows a *-?-Ricci-Bourguignon soliton, then the curvature tensor R with the soliton vector field V is given by the expression (Script capital LVR)(V-1,?)? = 2??{V1(r)? - V-1(Dr) + ?(Dr) - ?(r)? - Dr}. Next, we show that if an almost Kenmotsu manifold such that ? belongs to (?,-2)'-nullity distribution where ? < -1 acknowledges a *-?-Ricci-Bourguignon soliton satisfying O + ????[(r + 4n(2)) + {?(?(r)) - ?(Dr)}], then the manifold is Ricci-flat and is locally isometric to Hn+1(-4) x R-n. Moreover if the metric admits a gradient almost *-?-Ricci-Bourguignon soliton and ? leaves the scalar curvature r invariant on a Kenmotsu manifold, then the manifold is an ?-Einstein. Also, if a Kenmotsu metric represents an almost *-?-Ricci-Bourguignon soliton with potential vector field V is pointwise collinear with ?, then the manifold is an ?-Einstein.

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