Abstract. The authors prove the existence of Osserman manifolds with indefinite Kähler metric of nonnegative or nonpositive holomorphic sectional curvature which are not locally symmetric.
Osserman pseudo-Riemannian manifolds with diagonalizable Jacobi operators are studied. A classification of such manifolds is achieved under two conditions on the number of different eigenvalues of the Jacobi operators and their associated elgenspaces.
Abstract. The covariant derivative of the Kähler form of an almost pseudoHermitian or of an almost para-Hermitian manifold satisfies certain algebraic relations. We show, conversely, that any 3-tensor which satisfies these algebraic relations can be realized geometrically. MSC 2010: 53B05, 15A72, 53A15, 53B10, 53C07, 53C25
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.