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

作者：Vacaru Sergiu I^*

来源：Mediterranean Journal of Mathematics, 2015, 12(4): 1397-1427.

DOI：10.1007/s00009-014-0461-7

• Ricci flows
• almost Kahler structures
• Lie algebroids
• Lagrange mechanics
• Finsler geometry
• effective Einstein spaces

In this work we investigate Ricci flows of almost Kahler 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 Kahler-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.

• 出版日期2015-11