In this paper, we consider *-Ricci soliton in the frame-work of Kenmotsu manifolds. First, we prove that if (M, g) is a Kenmotsu manifold and g is a *-Ricci soliton, then soliton constant λ is zero. For 3-dimensional case, if M admits a *-Ricci soliton, then we show that M is of constant sectional curvature –1. Next, we show that if M admits a *-Ricci soliton whose potential vector field is collinear with the characteristic vector field ξ, then M is Einstein and soliton vector field is equal to ξ. Finally, we prove that if g is a gradient almost *-Ricci soliton, then either M is Einstein or the potential vector field is collinear with the characteristic vector field on an open set of M. We verify our result by constructing examples for both *-Ricci soliton and gradient almost *-Ricci soliton.

In this paper, we study contact metric manifold whose metric is a Riemann soliton. First, we consider Riemann soliton (g, V ) with V as contact vector field on a Sasakian manifold (M, g) an...

Ricci solitons (RS) have an extensive background in modern physics and are extensively used in cosmology and general relativity. The focus of this work is to investigate Ricci almost solitons (RAS) on Lorentzian manifolds with a special metric connection called a semi-symmetric metric $\mathbf{u}$-connection ($\mathcal{SSM}$-connection). First, we show that any quasi-Einstein Lorentzian manifold having a $\mathcal{SSM}$-connection, whose metric is RS, is Einstein manifold. A similar conclusion also holds for a Lorentzian manifold with $\mathcal{SSM}$-connection admitting RS whose soliton vector Z is parallel to the vector $\mathbf{u}$. Finally, we examine the gradient Ricci almost soliton (GRAS) on Lorentzian manifold admitting $\mathcal{SSM}$-connection.