On integral manifolds of an integrable nonlinear connection from the standpoint of the theory of Finsler connections (Q1191319)

In a previous paper of the author with \textit{L. Tamássy} [Demonstr. Math. 13, 551-564 (1980; Zbl 0444.53045)] the \(v(h)\)-torsion tensor \(R^ 1\) in a Finsler space \((M,L)\) is regarded as the curvature tensor of the nonlinear connection \(N\) and the vanishing of \(R^ 1\) is an integrability condition of \(N\), which is a distribution in the tangent bundle. In the present paper the author considers an integral manifold of the integrable non-linear connection \(N\) from the standpoint of the theory of Finsler connections. The tangent bundle \(T(M)\) becomes a Riemannian space with the metric which is obtained by lifting the Finslerian fundamental tensor. Thus the author develops a Riemannian geometrical subspace theory of integral manifolds obtaining the Gauss derivation formula, the Weingarten formula and the Gauss-Codazzi-Ricci equations.