Metric transformations under collapsing of Riemannian manifolds
Differential Geometry
2015-10-22 v2 Metric Geometry
Abstract
Let (M,g) be a Riemannian manifold with an isometric action of the Lie group G. Let g_G be a left invariant metric on G. Consider the diagonal G action on the product with the metric g+g_G. In this paper we calculate the formula for the metric h on the quotient space ; the map from g to h is the metric transformation. In particular when g is the hyperbolic metric on H^2 and G=S^1, the transformed metric h is Hamilton's cigar soliton metric studied in the Ricci flow.
Keywords
Cite
@article{arxiv.math/0303122,
title = {Metric transformations under collapsing of Riemannian manifolds},
author = {Bennett Chow and David Glickenstein and Peng Lu},
journal= {arXiv preprint arXiv:math/0303122},
year = {2015}
}
Comments
10 pages. This is a revised version with a new reference to previous work of Cheeger