Symmetry and local conjugacy on complex manifolds
The structure of the set S of all symmetric points in a complex manifold M with metric is studied (a\(\in M\) is called symmetric if a is isolated in the fixed point set of a biholomorphic isometry of M with period 2). In finite dimensions it is shown (actually for the bigger set of all pseudo-symmetric points) that S is a closed real-analytic submanifold of M and that any two points of a connected component of S are conjugate with respect to a biholomorphic isometry of M. In infinite dimensions counter-examples show that this result is not true in general. But it holds for the set of circular points.
scientific article; zbMATH DE number 4115000