Constant Curvature Coefficients and Exact Solutions in Fractional Gravity and Geometric Mechanics

Details Constant Curvature Coefficients and Exact Solutions in Fractional Gravity and Geometric Mechanics Constant Curvature Coefficients and Exact Solutions in Fractional Gravity and Geometric Mechanics

2010-07-16

arxiv.org/abs/1007.2864v3

Central European Journal of Physics 9 (2011) 1267-1279

Physics

Mathematical Physics

latex2e, 11pt, 27 pages, the variant accepted to CEJP; added and up-dated references

Scientific paper

10.2478/s11534-011-0040-5

We study fractional configurations in gravity theories and Lagrange mechanics. The approach is based on Caputo fractional derivative which gives zero for actions on constants. We elaborate fractional geometric models of physical interactions and we formulate a method of nonholonomic deformations to other types of fractional derivatives. The main result of this paper consists in a proof that for corresponding classes of nonholonomic distributions a large class of physical theories are modelled as nonholonomic manifolds with constant matrix curvature. This allows us to encode the fractional dynamics of interactions and constraints into the geometry of curve flows and solitonic hierarchies.

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