Riemannian geometry of ${\rm Diff}(S^1)/S^1$ and representations of the Virasoro algebra

Details Riemannian geometry of ${\rm Diff}(S^1)/S^1$ and representations of the Virasoro algebra Riemannian geometry of ${\rm Diff}(S^1)/S^1$ and representations of the Virasoro algebra

2005-10-28

arxiv.org/abs/math-ph/0510092v2

Physics

Mathematical Physics

Scientific paper

The main result of the paper is a computation of the Ricci curvature of
$\DS/S^1$. Unlike earlier results on the subject, we do not use the K\"{a}hler
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.

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