On boundaries of unions of sets with positive reach.
In this paper we study two classes of lightlike submanifolds of codimension two of semi-Riemannian manifolds, according as their radical subspaces are 1-dimensional or 2-dimensional. For a large variety of both these classes, we prove the existence of integrable canonical screen distributions subject to some reasonable geometric conditions and support the results through examples.
We classify generic Cauchy-Riemann submanifolds (of a Kaehlerian manifold) whose fundamental form is preserved by any local geodesic symmetry.
We study four-dimensional almost Kähler manifolds (M,g,J) which admit an opposite almost Kähler structure.
We prove that every compact balanced astheno-Kähler manifold is Kähler, and that there exists an astheno-Kähler structure on the product of certain compact normal almost contact metric manifolds.
For compact Kählerian manifolds, the holomorphic pseudosymmetry reduces to the local symmetry if additionally the scalar curvature is constant and the structure function is non-negative. Similarly, the holomorphic Ricci-pseudosymmetry reduces to the Ricci-symmetry under these additional assumptions. We construct examples of non-compact essentially holomorphically pseudosymmetric Kählerian manifolds. These examples show that the compactness assumption cannot be omitted in the above stated theorem....
In this paper the authors study compact homogeneous spaces (of a Lie group ) on which there if defined a -invariant symplectic form . It is an important feature of the paper that very little is assumed concerning and . The essential assumptions are: (1) is connected and (2) is uniform (i.e., is compact). Further, for convenience only and with no loss of generality, it is supposed that is simply connected and contains no connected normal subgroup of , i.e., that acts almost effectively...