Scalar curvature estimates for compact symmetric spaces
Differential Geometry
2008-09-16 v1
Abstract
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.
Cite
@article{arxiv.math/0010199,
title = {Scalar curvature estimates for compact symmetric spaces},
author = {S. Goette and U. Semmelmann},
journal= {arXiv preprint arXiv:math/0010199},
year = {2008}
}
Comments
13 pages, LaTeX, uses amsart