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Poisson structures on certain moduli spaces for bundles on a surface

Johannes Huebschmann (1995)

Annales de l'institut Fourier

Let Σ be a closed surface, G a compact Lie group, with Lie algebra g , and ξ : P Σ a principal G -bundle. In earlier work we have shown that the moduli space N ( ξ ) of central Yang-Mills connections, with reference to appropriate additional data, is stratified by smooth symplectic manifolds and that the holonomy yields a homeomorphism from N ( ξ ) onto a certain representation space Rep ξ ( Γ , G ) , in fact a diffeomorphism, with reference to suitable smooth structures C ( N ( ξ ) ) and C Rep ξ ( Γ , G ) , where Γ denotes the universal central extension of...

Prékopa–Leindler type inequalities on Riemannian manifolds, Jacobi fields, and optimal transport

Dario Cordero-Erausquin, Robert J. McCann, Michael Schmuckenschläger (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

We investigate Prékopa-Leindler type inequalities on a Riemannian manifold M equipped with a measure with density e - V where the potential V and the Ricci curvature satisfy Hess x V + Ric x λ I for all x M , with some λ . As in our earlier work [14], the argument uses optimal mass transport on M , but here, with a special emphasis on its connection with Jacobi fields. A key role will be played by the differential equation satisfied by the determinant of a matrix of Jacobi fields. We also present applications of the method...

Projectively flat Finsler metrics with orthogonal invariance

Libing Huang, Xiaohuan Mo (2013)

Annales Polonici Mathematici

We study Finsler metrics with orthogonal invariance. By determining an expression of these Finsler metrics we find a PDE equivalent to these metrics being locally projectively flat. After investigating this PDE we manufacture projectively flat Finsler metrics with orthogonal invariance in terms of error functions.

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