Riemannian geometry of \rm Diff(S¹)/S¹ and representations of the Virasoro algebra

2005/10/28 by Maria Gordina, M. Gordina, Gordina, M. +3
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math-ph #math.DG #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/0510092

arxiv created 2005/11/19 · arxiv updated 2009/12/01

Abstract

The main result of the paper is a computation of the Ricci curvature of \DS/S¹. Unlike earlier results on the subject, we do not use the Kähler structure symmetries to compute the Ricci curvature, but rather rely on classical finite-dimensional results of Nomizu et al on Riemannian geometry of homogeneous spaces.

Citations

• Curvatures of left invariant metrics on lie groups

Related

• Curvature of the Virasoro-Bott group
• Ricci pinched compact submanifolds in space forms
• The Batalin-Vilkovisky formalism with the Virasoro symmetry
• Riemannian Geometry of C^1,1 Manifolds
• Manifolds with A Lower Ricci Curvature Bound