On pseudosymmetric para-Kählerian manifolds.
Results on derivations and automorphisms of some quantum and classical Poisson algebras, as well as characterizations of manifolds by the Lie structure of such algebras, are revisited and extended. We prove in particular a somewhat unexpected fact that the algebras of linear differential operators acting on smooth sections of two real vector bundles of rank 1 are isomorphic as Lie algebras if and only if the base manifolds are diffeomorphic, whether or not the line bundles themselves are isomorphic....
In this paper a Weil approach to quasijets is discussed. For given manifolds and , a quasijet with source and target is a mapping which is a vector homomorphism for each one of the vector bundle structures of the iterated tangent bundle [A. Dekrét, Casopis Pest. Mat. 111, No. 4, 345-352 (1986; Zbl 0611.58004)]. Let us denote by the bundle of quasijets from to ; the space of non-holonomic -jets from to is embeded into . On the other hand, the bundle of -quasivelocities...
In this paper we survey some recent results on rank one symmetric space.
We show that any real Kähler Euclidean submanifold with either non-negative Ricci curvature or non-negative holomorphic sectional curvature has index of relative nullity greater than or equal to . Moreover, if equality holds everywhere, then the submanifold must be a product of Euclidean hypersurfaces almost everywhere, and the splitting is global provided that is complete. In particular, we conclude that the only real Kähler submanifolds in that have either positive Ricci curvature or...