https://neckpinch.com/authors/akhilesh-yadav/New arXiv papers by Akhilesh Yadav, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2510.16011arxiv:2510.16011Wed, 15 Oct 2025 00:00:00 GMTAkhilesh Yadav, Tarun Saxena — The aim of this paper is to study geometrical aspects of static spacetime admitting an almost gradient Ricci soliton. Among others, We first determine the conditions under which the base manifold of static spacetime possess an almost gradient Ricci soliton and we show that the almost gradient Ricci soliton become steady gradient Ricci soliton when static spacetime turns to a vacuum static spacetime. Next, we exhibit that an expanding almost gradient Ricci soliton on base manifold of non-compact and connected static spacetime satisfies shrodinger's equation for a smooth function f. Also, we find the soliton constant under which the static perfect fluid spacetime with almost gradient Ricci soliton holds the null convergence condition and the strong energy condition. Further, we study the almost gradient Ricci soliton on base manifold of static perfect fluid spacetime with potential function as warping function and it is shown that the base manifold of a static perfect fluid spacetime with an almost gradient Ricci soliton is an Einstein manifold. Next, we obtain a necessary and sufficient condition on soliton constant to obey timelike convergence condition. Further, we obtain some results for Ricci symmetric and weakly Ricci symmetric base manifold of static perfect fluid spacetime admitting gradient Ricci soliton. Finally, we find the nature of almost gradient Ricci soliton on 4-dimensional half conformally flat base manifold of static perfect fluid spacetime.Ricci solitonsEinstein metricsAlmost & η-Ricci solitonsBoundaries & non-compact https://arxiv.org/abs/2203.00683arxiv:2203.00683Tue, 01 Mar 2022 00:00:00 GMTKiran Meena, Akhilesh Yadav — In this paper, we study conformal submersions from Ricci solitons to Riemannian manifolds with non-trivial examples. First, we study some properties of the O'Neill tensor A in the case of conformal submersion. We also find a necessary and sufficient condition for conformal submersion to be totally geodesic and calculate the Ricci tensor for the total manifold of such a map with different assumptions. Further, we consider a conformal submersion F:M → N from a Ricci soliton to a Riemannian manifold and obtain necessary conditions for the fibers of F and the base manifold N to be Ricci soliton, almost Ricci soliton and Einstein. Moreover, we find necessary conditions for a vector field and its horizontal lift to be conformal on N and (KerF_∗)^bot, respectively. Also, we calculate the scalar curvature of Ricci soliton M. Finally, we obtain a necessary and sufficient condition for F to be harmonic.Ricci solitonsAlmost & η-Ricci solitonsScalar curvature https://arxiv.org/abs/2108.01449arxiv:2108.01449Mon, 02 Aug 2021 00:00:00 GMTKiran Meena, Akhilesh Yadav — In this paper, first we define Clairaut Riemannian map between Riemannian manifolds by using a geodesic curve on the base space and find necessary and sufficient conditions for a Riemannian map to be Clairaut with a non-trivial example. We also obtain necessary and sufficient condition for a Clairaut Riemannian map to be harmonic. Thereafter, we study Clairaut Riemannian map from Riemannian manifold to Ricci soliton with a non-trivial example. We obtain scalar curvatures of rangeF_∗ and (rangeF_∗)^bot by using Ricci soliton. Further, we obtain necessary conditions for the leaves of rangeF_∗ to be almost Ricci soliton and Einstein. We also obtain necessary condition for the vector field dotβ to be conformal on rangeF_∗ and necessary and sufficient condition for the vector field dotβ to be Killing on (rangeF_∗)^bot, where β is a geodesic curve on the base space of Clairaut Riemannian map. Also, we obtain necessary condition for the mean curvature vector field of rangeF_∗ to be constant. Finally, we introduce Clairaut anti-invariant Riemannian map from Riemannian manifold to Kähler manifold, and obtain necessary and sufficient condition for an anti-invariant Riemannian map to be Clairaut with a non-trivial example. Further, we find necessary condition for rangeF_∗ to be minimal and totally geodesic. We also obtain necessary and sufficient condition for Clairaut anti-invariant Riemannian maps to be harmonic.Ricci solitonsAlmost & η-Ricci solitonsKähler geometryScalar curvature