Spectral Functionals, Nonholonomic Dirac Operators, and Noncommutative
Ricci Flows
Sergiu I. Vacaru,
2008.06.24
http://arxiv.org/abs/0806.3814
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.
