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Almost Kähler Ricci Flows and Einstein and Lagrange-Finsler Structures on Lie Algebroids

Vacaru, Sergiu

In: Mediterranean Journal of Mathematics, 2015, vol. 12, no. 4, p. 1397-1427

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    Titre
    • Almost Kähler Ricci Flows and Einstein and Lagrange-Finsler Structures on Lie Algebroids
    Auteur
    • Vacaru, Sergiu. Theory Division, CERN, 1211, Geneva 23, Switzerland
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Mediterranean Journal of Mathematics, 2015, vol. 12, no. 4, p. 1397-1427. Springer Basel
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:331082
    Summary
    In this work we investigate Ricci flows of almost Kähler 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, some examples of generic off-diagonal solutions for Lie algebroid-type Ricci solitons and (effective) Einstein and Lagrange-Finsler algebroids are provided.