Extension of the interior connection of a nonholonomic manifold with a Finsler metric

TL;DR

This paper introduces extended truncated connections on nonholonomic manifolds with Finsler metrics, establishing their uniqueness in contact spaces and relating their curvature to Wagner's tensor in sub-Riemannian geometry.

Contribution

It defines a new class of extended truncated connections and proves their uniqueness in contact Finsler spaces, linking curvature tensors to Wagner's tensor.

Findings

Existence of a unique extended truncated connection in contact Finsler spaces.

The curvature tensor coincides with Wagner's tensor in sub-Riemannian spaces.

Extension of interior connection concepts to nonholonomic manifolds with Finsler metrics.

Abstract

The notions of the interior and truncated connections of a nonholonomic manifold are introduced. A class of extended truncated connections is distinguished. For the case of a contact space with a Finsler metric, it is shown that there exists a unique extended truncated connection that satisfies additional properties. The curvature tensor of the obtained connection in the case of a sub-Riemannian space coincides with the Wagner curvature tensor that was constructed by Wagner for the case of an arbitrary nonholonomic manifold of codimension one endowed with an interior affine connection.