A mechanics for the Ricci flow

S. Abraham; P. Fernandez de Cordoba; J. M. Isidro; J. L. G. Santander

doi:10.1142/S0219887809003825

A mechanics for the Ricci flow

High Energy Physics - Theory 2009-10-16 v3

Authors: S. Abraham , P. Fernandez de Cordoba , J. M. Isidro , J. L. G. Santander

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Abstract

We construct the classical mechanics associated with a conformally flat Riemannian metric on a compact, n-dimensional manifold without boundary. The corresponding gradient Ricci flow equation turns out to equal the time-dependent Hamilton-Jacobi equation of the mechanics so defined.

Keywords

hamiltonian mechanics differential geometry in physics

Cite

@article{arxiv.0810.2356,
  title  = {A mechanics for the Ricci flow},
  author = {S. Abraham and P. Fernandez de Cordoba and J. M. Isidro and J. L. G. Santander},
  journal= {arXiv preprint arXiv:0810.2356},
  year   = {2009}
}