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.

This article presents a novel parametrization of the deceleration parameter (DP) to investigate the cosmological scenario. The newly proposed parametric form of the DP is both physically plausible and model-independent. Constrained by a combined dataset of 31 cosmic chronometers (CC) data points, 26 non-correlated baryonic acoustic oscillations (BAO) points, and 1701 Pantheon $$+$$+ data points from supernovae type Ia (SNeIa), we determine the model parameters using a Markov Chain Monte Carlo (MCMC) method. The analysis explores the kinematic behavior of the model, including the transition from deceleration to acceleration. The results indicate that the Universe is currently in an accelerated phase. Furthermore, we apply the obtained parameter values to constrain f(Q) gravity models and compare them with observations. This study provides valuable insights into the accelerating Universe and underscores the importance of employing a model-independent approach in cosmological investigations.

We consider almost $$*$$∗ -Ricci solitons in the context of paracontact geometry, precisely, on a paraKenmotsu manifold. First, we prove that if the metric g of $$\eta $$η -Einstein paraKenmotsu manifold is $$*$$∗ Ricci soliton, then M is Einstein. Next, we show that if $$\eta $$η -Einstein paraKenmotsu manifold admits a gradient almost $$*$$∗ -Ricci soliton, then either M is Einstein or the potential vector field collinear with Reeb vector field $$\xi $$ξ . Finally, for three-dimensional case we show that paraKenmotsu manifold is of constant curvature $$-1$$- 1 . An illustrative example is given to support the obtained results.