2011/08/31 by Laurenţiu Bubuianu, Sergiu I. Vacaru
Mathematics · Medicine · Physics and Astronomy · #Advanced Differential Geometry Research #Classical mechanics #Computer science #Flow (mathematics) #Geometric Analysis and Curvature Flows #Geometry #Lagrange multiplier #Lie group #Mathematical physics #Mathematics #Mechanics #Nonholonomic system #Ophthalmology and Eye Disorders #Physics #Pure mathematics #Quantum mechanics #Ricci curvature #Ricci flow #math-ph #math.DG #math.MP #msc:17B66 #msc:37J60 #msc:53C44 #msc:53D17 #msc:70G45 #msc:70S05
paper · pdf · doi:10.1139/cjp-2018-0158
published as Canadian J. Phys. 97 (2019) 133-144 · latex2e, 11pt, 25 pages, v3 substantially modified with a changed title and new co-author - accepted to Can. J. Phys
arxiv created 2018/05/27 · openalex publication_date 2018/05/28 · openalex created_date 2018/06/01 · arxiv updated 2019/02/25 · openalex updated_date 2026/08/05
The approach to nonholonomic Ricci flows and geometric evolution of regular Lagrange systems (S. Vacaru. J. Math. Phys. 49, 043504 (2008); Ibid. Rep. Math. Phys. 63, 95 (2009)) is extended to include geometric mechanics and gravity models on Lie algebroids. We prove that such evolution scenarios of geometric mechanics and analogous gravity can be modeled as gradient flows characterized by generalized Perelman functionals if an equivalent geometrization of Lagrange mechanics (J. Kern. Arch. Math. (Basel), 25, 438 (1974)) is considered. The Hamilton equations on Lie algebroids describing Lagrange–Ricci flows are derived. Finally, we show that geometric evolution models on Lie algebroids are described by effective thermodynamical values derived from statistical functionals on prolongation Lie algebroids.