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Ricci Flow of 3-D Manifolds with One Killing Vector | | J. Gegenberg
; G. Kunstatter
; | | Date: |
29 Sep 2004 | | Subject: | hep-th | | Affiliation: | U. of New Brunswick) and G. Kunstatter (U. of Winnipeg | | Abstract: | We implement a suggestion by Bakas and consider the Ricci flow of 3-d manifolds with one Killing vector by dimensional reduction to the corresponding flow of a 2-d manifold plus scalar (dilaton) field. By suitably modifying the flow equations in order to make them manifestly parabolic, we are able to show that the equations for the 2-d geometry can be put in the form explicitly solved by Bakas using a continual analogue of the Toda field equations. The only remaining equation, namely that of the scale factor of the extra dimension, is a linear equation that can be readily solved using standard techniques once the 2-geometry is specified. We illustrate the method with a couple of specific examples. | | Source: | arXiv, hep-th/0409293 | | Services: | Forum | Review | PDF | Favorites | |
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