Spectral Functionals, Nonholonomic Dirac Operators, and Noncommutative Ricci Flows
Mathematical Physics
2011-06-02 v3 General Relativity and Quantum Cosmology
High Energy Physics - Theory
Differential Geometry
math.MP
Abstract
We formulate a noncommutative generalization of the Ricci flow theory in the framework of spectral action approach to noncommutative geometry. Grisha Perelman's functionals are generated as commutative versions of certain spectral functionals defined by nonholonomic Dirac operators and corresponding spectral triples. We derive the formulas for spectral averaged energy and entropy functionals and state the conditions when such values describe (non)holonomic Riemannian configurations.
Cite
@article{arxiv.0806.3814,
title = {Spectral Functionals, Nonholonomic Dirac Operators, and Noncommutative Ricci Flows},
author = {Sergiu I. Vacaru},
journal= {arXiv preprint arXiv:0806.3814},
year = {2011}
}
Comments
latex2e, 11pt, 40 pages, v3, version accepted for publication in JMP, modified following referee's recommendations, new affiliation and updated references