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Open Access. Click on the DOI link to access the article at the publisher's website.We study fixed point sets for holomorphic automorphisms(and endomorphisms) on complex manifolds. The mainobject of our interest is to determine the number and configurationof fixed points that forces an automorphism (endomorphism)to be the identity. These questions have been examined in a numberof papers for a bounded domain in Cn. Here we resolve the casefor a general finite dimensional hyperbolic manifold. We also showthat the results for non-hyperbolic manifolds are notably different.Peer reviewe

Fixed points and determining sets for holomorphic self-maps of a hyperbolic manifold