Geometric superrigidity. (English) Zbl 0808.53043

The most general results in the theory of geometric superrigidity are proved. The proof of these results consists of a general Bochner type formula obtained by a simple integration by parts and of the verification of certain inequalities for the eigenvalues of a certain quadratic form defined from the invariant curvature tensor.


53C20 Global Riemannian geometry, including pinching
58J60 Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
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