Rotations and Hermitian symmetric spaces
On an almost Hermitian manifold (M,g,J) one considers the naturally defined field of local diffeomorphisms (J-rotations) \(j_ m=\exp_ m\circ J_ m\circ \exp_ m^{-1}\), \(m\in M\), and in particular, one studies isometric, harmonic, holomorphic and symplectic J-rotations. This leads to some characterizations of special classes of almost Hermitian manifolds, including the class of Hermitian symmetric spaces. In addition, one treats some properties of the shape operator (extrinsic geometry) and of the Ricci operator (intrinsic geometry) of a geodesic sphere relating to the J-rotations.
scientific article; zbMATH DE number 4171863
scientific article