2013/06/30 by Sergiu I. Vacaru · 2 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Computer science #Einstein #Finsler manifold #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Lie algebra #Lie algebroid #Mathematical analysis #Mathematical physics #Mathematics #Nonholonomic system #Pure mathematics #Ricci curvature #Ricci flow #Symplectic geometry #Type (biology) #gr-qc #math-ph #math.DG #math.MP #msc:37J60 #msc:53B35 #msc:53B40 #msc:53C44 #msc:53D15 #msc:53D17 #msc:70G45 #msc:70S05 #msc:83D99
paper · pdf · doi:10.1007/s00009-014-0461-7
published as Mediterr. J. Math. 12 (2015) 1397-1427 · This version is accepted by Mediterranian J. Math. and modified following editor/referee's requests. File latex2e 11pt generates 29 pages
arxiv created 2014/09/01 · openalex publication_date 2014/09/09 · arxiv updated 2016/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this work we investigate Ricci flows of almost Kaehler structures on Lie algebroids when the fundamental geometric objects are completely determined by (semi) Riemannian metrics, or effective) regular generating Lagrange/ Finsler, functions. There are constructed canonical almost symplectic connections for which the geometric flows can be represented as gradient ones and characterized by nonholonomic deformations of Grigory Perelman's functionals. The first goal of this paper is to define such thermodynamical type values and derive almost Kähler - Ricci geometric evolution equations. The second goal is to study how fixed Lie algebroid, i.e. Ricci soliton, configurations can be constructed for Riemannian manifolds and/or (co) tangent bundles endowed with nonholonomic distributions modelling (generalized) Einstein or Finsler - Cartan spaces. Finally, there are provided some examples of generic off-diagonal solutions for Lie algebroid type Ricci solitons and (effective) Einstein and Lagrange-Finsler algebroids.