Finsler connections in anholonomic geometry of a Kropina space. (English) Zbl 0996.53019

This is a continuation of two papers: D. Hrimiuc and H. Shimada, Nonlinear World 3, No. 4, 613-641 (1996; Zbl 0894.53029) and P. L. Antonelli and I. Bucataru, in L. Kozma (ed.) et al., Proc. of the Colloquium on differential geometry, Debrecen, Hungary, 2000, 39-54 (2001; Zbl 0985.53018)]. Consider \(\alpha(x,y)= (a_{ij}(x)y^i y^j)^{1/2}\) and \(\beta (x,y) =b_i(x)y^i\) on the tangent bundle \(TM\), and define a Kropina function \(F(x,y)= \alpha^2 (x,y)/ |\beta (x,y)|\). The pair \((M,F)\) is a Finsler space, called Kropina space.


53B40 Local differential geometry of Finsler spaces and generalizations (areal metrics)
53B20 Local Riemannian geometry
58B20 Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds
53C80 Applications of global differential geometry to the sciences