Local rigidity of symmetric spaces

Schroeder, V.; Ziller, W.

doi:10.1090/S0002-9947-1990-0958901-X

Local rigidity of symmetric spaces
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by V. Schroeder and W. Ziller PDF

Trans. Amer. Math. Soc. 320 (1990), 145-160 Request permission

Abstract:

We show that on a symmetric space of noncompact or compact type the metric is locally rigid in the sense that if one changes the metric locally but preserves the curvature bounds, then the new metric is isometric to the old one. We also prove an analytic continuation property for symmetric spaces of rank $\ge 3$.

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