Chern's orthonormal frame bundle of a Finsler space (Q2716462)

Let \((M,F)\) a strongly convex Finsler space, \(\dim M=n\) and \(O_F(M)\) be Chern's orthonormal frame bundle. The author defines the notion of nonlinear connection on the manifold \(O_F(M)\) and proves the following important results:NEWLINENEWLINENEWLINEa) There exists on \(O_F(M)\) a unique torsion-free nonlinear connection \(N\);NEWLINENEWLINENEWLINEb) \(N\) coincides with Chern's connection of the Finsler space \((M,F)\).NEWLINENEWLINENEWLINEThese results lead to a new geometrical interpretation of Chern connection and to a simplified proof of the Chern's Theorem: The group of isometries of the space \((M,F)\) is a Lie group of dimension less or equal to \({1\over 2}n(n+1)\).NEWLINENEWLINENEWLINEThe paper contains several other interesting results.