Rotations and Hermitian symmetric spaces

On an almost Hermitian manifold (M, g, J) one considers the naturally defined field of local diffeomorphismsj _m =exp _m J _m exp _m ^–1 ,mM, and in particular, one studies isometric, harmonic, holomorphic and symplecticj _m . This leads to some characterizations of special classes of almost Hermitian manifolds, including the class of Hermitian symmetric spaces. In addition, one treats some intrinsic and extrinsic geometrical properties of geodesic spheres relating to these local diffeomorphisms.Supported by grant 203.01.50 of the C.N.R., Italy.