### Invariant differential operators and Frobenius decomposition of a $G$-variety. (Invariante Differentialoperatoren und die Frobenius-Zerlegung einer $G$-Varietät.)

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This review article intends to introduce the reader to non-integrable geometric structures on Riemannian manifolds and invariant metric connections with torsion, and to discuss recent aspects of mathematical physics—in particular superstring theory—where these naturally appear. Connections with skew-symmetric torsion are exhibited as one of the main tools to understand non-integrable geometries. To this aim a a series of key examples is presented and successively dealt with using the notions of...

We prove that the ring ℝ[M] of all polynomials defined on a real algebraic variety $M\subset {\mathbb{R}}^{n}$ is dense in the Hilbert space ${L}^{2}(M,{e}^{-{\left|x\right|}^{2}}d\mu )$, where dμ denotes the volume form of M and $d\nu ={e}^{-{\left|x\right|}^{2}}d\mu $ the Gaussian measure on M.

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