Identifying Constant Curvature Manifolds, Einstein Manifolds, and Ricci Parallel Manifolds

2017/10/01 by Feng‐Yu Wang, Wang, Feng-Yu
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1710.00276

openalex publication_date 2017/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We establish variational formulas for Ricci upper and lower bounds, as well as a derivative formula for the Ricci curvature. As applications, constant curvature manifolds, Einstein manifolds and Ricci parallel manifolds are identified, respectively, with different integral-differential formulas and semigroup inequalities. Moreover, by using derivative and Hessian formulas for the heat semigroup P_t developed from stochastic analysis, explicit Hessian estimates are derived on Einstein and Ricci parallel manifolds.

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