When G is a complex reductive algebraic group and G/K is a reductive symmetric space, the decomposition of C[G/K] as a K-module was obtained (in a non-constructive way) by R. Richardson, generalizing the celebrated result of Kostant-Rallis for the linearized problem (the harmonic decomposition of the isotropy representation). To obtain a constructive version of Richardson’s results, this paper ...

Let $M$ is a (pseudo-)Riemannian manifold and $TM$ be its tangent bundlewith the semi-symmetric metric connection $\overline{\nabla }$. In thispaper, we examine some special vector fields, such as incompressible vectorfields, harmonic concurrent conformal vectorfields projective fields on with respect to thesemi-symmetric }$ obtain someproperties related them.

We develop a harmonic analysis on objects of some category C 2 of infinite-dimensional filtered vector spaces over a finite field. It includes two-dimensional local fields and adelic spaces of algebraic surfaces defined over a finite field. The main result is the theory of the Fourier transform on these objects and two-dimensional Poisson formulas.

Using the characterization of last multipliers as solutions of the Liouville’s transport equation, new results are given in this approach of ODE by providing several new characterizations, e.g. in terms of Witten and Marsden differentials or adjoint vector field. Applications to Hamiltonian vector fields on Poisson manifolds and vector fields on Riemannian manifolds are presented. In Poisson ca...

For a smooth, bounded, pseudoconvex domain Ω ⊂ C n , we derive a new sufficient condition for global regularity of the ¯ ∂-Neumann operator that generalizes McNeal's Property (˜ P), the approximately holomorphic vector fields of Boas and Straube, and a condition involving bounded plurisub-harmonic exhaustion functions due to Kohn.

We develop a harmonic analysis on objects of some category C 2 of infinite-dimensional filtered vector spaces over a finite field. It includes two-dimensional local fields and adelic spaces of algebraic surfaces defined over a finite field. The main result is the theory of the Fourier transform on these objects and two-dimensional Poisson formulas.

In this paper we show, in a systematic way, how to relate the Kepler problem to the isotropic harmonic oscillator. Unlike previous approaches, our constructions are carried over in the Lagrangian formalism dealing, with second order vector fields. We therefore provide a tangent bundle version of the Kustaanheimo-Stiefel map.

Recently, we have used the symmetric bracket of vector fields, and developed the notion of the symmetric derivation. Using this machinery, we have defined the concept of symmetric curvature. This concept is natural and is related to the notions divergence and Laplacian of vector fields. This concept is also related to the derivations on the algebra of symmetric forms which has been discu...