https://neckpinch.com/authors/pinaki-ranjan-ghosh/New arXiv papers by Pinaki Ranjan Ghosh, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2001.07965/arxiv:2001.07965Wed, 22 Jan 2020 00:00:00 GMTAbsos Ali Shaikh, Prosenjit Mandal, Chandan Kumar Mondal, Pinaki Ranjan Ghosh — Cartan-Hadamard manifold is a simply connected Riemannian manifold with non-positive sectional curvature. In this article, we have proved that a Cartan-Hadamard manifold satisfying steady gradient Ricci soliton with the integral condition of potential function is isometric to the Euclidean space. Next we have proved a compactness theorem for gradient shrinking Ricci soliton satisfying some scalar curvature condition. Finally, we have showed that a gradient expanding Ricci soliton with linear volume growth and positive potential function is an Einstein manifold.Ricci solitonsEinstein metricsSphere theoremsScalar curvatureLimit spaces & RCD