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On quantum and classical Poisson algebras

Janusz Grabowski, Norbert Poncin (2007)

Banach Center Publications

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....

On quasijet bundles

Tomáš, Jiří (2000)

Proceedings of the 19th Winter School "Geometry and Physics"

In this paper a Weil approach to quasijets is discussed. For given manifolds M and N , a quasijet with source x M and target y N is a mapping T x r M T y r N which is a vector homomorphism for each one of the r vector bundle structures of the iterated tangent bundle T r [A. Dekrét, Casopis Pest. Mat. 111, No. 4, 345-352 (1986; Zbl 0611.58004)]. Let us denote by Q J r ( M , N ) the bundle of quasijets from M to N ; the space J ˜ r ( M , N ) of non-holonomic r -jets from M to N is embeded into Q J r ( M , N ) . On the other hand, the bundle Q T m r N of ( m , r ) -quasivelocities...

On rank one symmetric space

Inkang Kim (2004/2005)

Séminaire de théorie spectrale et géométrie

In this paper we survey some recent results on rank one symmetric space.

On real Kähler Euclidean submanifolds with non-negative Ricci curvature

Luis A. Florit, Wing San Hui, F. Zheng (2005)

Journal of the European Mathematical Society

We show that any real Kähler Euclidean submanifold f : M 2 n 2 n + p with either non-negative Ricci curvature or non-negative holomorphic sectional curvature has index of relative nullity greater than or equal to 2 n 2 p . Moreover, if equality holds everywhere, then the submanifold must be a product of Euclidean hypersurfaces almost everywhere, and the splitting is global provided that M 2 n is complete. In particular, we conclude that the only real Kähler submanifolds M 2 n in 3 n that have either positive Ricci curvature or...

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