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Geometric flows and applications
Author(s) -
Petropoulos P.M.
Publication year - 2010
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.201000059
Subject(s) - general relativity , string theory , ricci flow , gravitation , string (physics) , homogeneous , flow (mathematics) , theoretical physics , dimension (graph theory) , property (philosophy) , mathematics , instanton , physics , classical mechanics , geometry , pure mathematics , mathematical physics , statistical physics , ricci curvature , curvature , philosophy , epistemology
I present some applications of geometric flows in string theory and gravity. In some circumstances time evolution in string theory can be approximately identified with Ricci‐flow parametric evolution of spatial sections. In four dimensions, homogeneous, self‐dual, gravitational instantons of general relativity evolve in time exactly as geometric flows of homogeneous three‐manifolds. For non‐relativistic versions of gravity, this property persists in any dimension, under the assumption of detailed‐balance condition.