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arXiv · 1710.00276

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

Feng-Yu Wang
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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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Feng-Yu Wang. 2017-11-25. Identifying Constant Curvature Manifolds, Einstein Manifolds, and Ricci Parallel Manifolds. https://arxiv.org/abs/1710.00276

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