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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.

MSC:
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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