Isometric, holomorphic and symplectic reflections
The authors study local reflections in Riemannian, almost Hermitian and Kählerian manifolds with respect to topologically embedded submanifolds. The assumptions that these reflections are isometric, or holomorphic, or symplectic (or combinations of these assumptions) have a strong influence on the intrinsic and extrinsic geometry of the corresponding submanifolds. Typically, they are proved to be totally geodesic, or holomorphic, or having both properties, according to the situation. Some technical results in this paper (derived by the method of Jacobi vector fields) seem to be of interest for themselves and waiting for other applications.
scientific article; zbMATH DE number 4102033
scientific article