arXiv subjects

Sayoojya Prakash

Publications and source records attributed to Sayoojya Prakash.

3 recordsLinked to original sources

arXiv2026

Ricci solitons as critical points of quadratic curvature functionals

Rigidity, stability and local minimizing properties of Einstein metrics as critical points of quadratic Riemannian functionals defined by $L^2$-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.

math.DG↗

arXiv2026

Rigidity of conformal submersions and quasi-Einstein manifolds

In this paper, we study two notions of rigidity, one of conformal submersions and the other of quasi Einstein manifolds, with an attempt to relate the two notions. Note that a smooth submersion between Riemannian manifolds is called conformal if it restricts to a conformal isometry on the horizontal distribution. A conformal submersion is said to be rigid if it reduces to a Riemannian submersion up to homothety. On the other hand, quasiEinstein manifolds are generalizations of Einstein manifolds that are of interest both in Riemannian geometry and theoretical physics. A Riemannian manifold $(M, g)$ is called quasi-Einstein if its Ricci tensor satisfies the identity: $R i c_g+ H e s s(f)-\frac{1}{m} d f \otimes d f=λg$ for some $f \in C^{\infty}(M)$ and constants $λ\in \mathbb{R}$ and $0 0$. In particular, we study curvature conditions that force conformal submersions to be rigid, also leading to the rigidity of a related class of quasi-Einstein manifolds.

math.DG↗

arXiv2026

Quasi-Einstein Metrics and a curvature identity associated with the Ricci flow

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.

math.DG↗