Scalar curvature estimates for compact symmetric spaces

Details Scalar curvature estimates for compact symmetric spaces Scalar curvature estimates for compact symmetric spaces

2000-10-20

arxiv.org/abs/math/0010199v1

Diff. Geom. Appl. 16 (2002), 65-78

Mathematics

Differential Geometry

13 pages, LaTeX, uses amsart

Scientific paper

10.1016/S0926-2245(01)00068-7

We establish extremality of Riemannian metrics g with non-negative curvature operator on symmetric spaces M=G/K of compact type with rk(G)-rk(K)\le 1. Let g' be another metric with scalar curvature k', such that g'\ge g on 2-vectors. We show that k'\ge k everywhere on M implies k'=k. Under an additional condition on the Ricci curvature of g, k'\ge k even implies g'=g. We also study area-non-increasing spin maps onto such Riemannian manifolds.

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