Ricci solitons as critical points of quadratic curvature functionals

Atreyee Bhattacharya; Sayoojya Prakash

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arXiv · 2606.13066

Ricci solitons as critical points of quadratic curvature functionals

Atreyee Bhattacharya·Sayoojya Prakash

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Abstract

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.

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Atreyee Bhattacharya, Sayoojya Prakash. 2026-06-11. Ricci solitons as critical points of quadratic curvature functionals. https://arxiv.org/abs/2606.13066

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