Rigidity of compact rank one symmetric spaces

2024/06/01 by Connell, Chris, Islam, Mitul, Nguyen, Thang +1
#53C24 (Primary) 53C20 #53C35 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2406.00558

Abstract

We consider rigidity properties of compact symmetric spaces X with metric g₀ of rank one. Suppose g is another Riemannian metric on X with sectional curvature κ bounded by 0 ≤ κ≤ 1. If g equals g₀ outside a convex proper subset of X, then g is isometric with g₀. We also exhibit examples of surfaces showing that the nonnegativity of the curvature is needed. Our main result complements earlier results on other symmetric spaces by Gromov and Schroeder-Ziller.

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