SCALAR CURVATURE ESTIMATES FOR COMPACT SYMMETRIC SPACES

@inproceedings{Goette2002SCALARCE,
  title={SCALAR CURVATURE ESTIMATES FOR COMPACT SYMMETRIC SPACES},
  author={Sebastian Goette and Uwe Semmelmann},
  year={2002}
}
We establish extremality of Riemannian metrics g with non-negative curvature operator on symmetric spaces M=G/K of compact type with rkG−rkK⩽1. Let ḡ be another metric with scalar curvature κ, such that g⩾g on 2-vectors. We show that κ⩾κ everywhere on M implies κ=κ. Under an additional condition on the Ricci curvature of g, κ⩾κ even implies g=g. We also study area-non-increasing spin maps onto such Riemannian manifolds. 

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