Scalar curvature estimates for compact symmetric spaces

✍ Scribed by S. Goette; U. Semmelmann

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 134 KB
• Volume: 16
• Category: Article
• ISSN: 0926-2245
• DOI: 10.1016/s0926-2245(01)00068-7

✦ Synopsis

We establish extremality of Riemannian metrics g with non-negative curvature operator on symmetric spaces M = G/K of compact type with rk Grk K 1. Let ḡ be another metric with scalar curvature κ, such that ḡ 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 ḡ = g. We also study area-non-increasing spin maps onto such Riemannian manifolds.