https://neckpinch.com/authors/sayoojya-prakash/New arXiv papers by Sayoojya Prakash, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2606.13066/arxiv:2606.13066Thu, 11 Jun 2026 00:00:00 GMTAtreyee Bhattacharya, Sayoojya Prakash — Rigidity, stability and local minimizing properties of Einstein metrics as critical points of quadratic Riemannian functionals defined by L²-norms of Ricci curvature, scalar curvature, Weyl curvature and Riemannian curvature have been extensively studied. However, there are non-Einstein critical points of these functionals that are not so well understood. In this paper, we study Ricci solitons, a generalization of Einstein metrics, that are critical points of a special quadratic curvature functional and analyze their rigidity.Ricci solitonsEinstein metricsScalar curvatureStability & uniqueness https://neckpinch.com/papers/2511.12144/arxiv:2511.12144Sat, 15 Nov 2025 00:00:00 GMTAtreyee Bhattacharya, Sayoojya Prakash — Quasi-Einstein manifolds are well-studied generalizations of Einstein manifolds. This includes gradient Ricci solitons and has a natural correspondence with the warped product Einstein manifolds. A quasi-Einstein metric is said to be rigid when it reduces to an Einstein metric. On a different note, Einstein metrics can be viewed as fixed points of the Ricci flow up to homothety. While gradient Ricci solitons are generalized fixed points of the Ricci flow, not much is known, in general, about the evolution of quasi-Einstein metrics under the Ricci flow. In this paper, we employ an identity associated to the evolution of curvature along the Ricci flow, to conclude the rigidity of certain closed quasi-Einstein manifolds.Ricci flowRicci solitonsEinstein metricsAlmost & η-Ricci solitonsStability & uniquenessRotational symmetry & warped products