Metrical Multi-Time Lagrange Geometry of Physical Fields

TL;DR

This paper develops a generalized geometric framework for physical fields using metrical multi-time Lagrange geometry on 1-jet bundles, extending classical Lagrangian theories to multi-time settings.

Contribution

It introduces a novel geometric approach to physical fields based on multi-time Lagrangian geometry, generalizing classical methods by Miron and Anastasiei.

Findings

Provides a natural geometric theory of physical fields on 1-jet bundles.

Extends classical Lagrangian geometry to multi-time contexts.

Lays groundwork for further applications in physics and geometry.

Abstract

The author exposes the metrical multi-time Lagrange geometry of physical fields which naturally generalizes the classical Lagrangian developped by Miron and Anastasiei. In other words, one constructs a natural theory of physical fields on the 1-jet fibre bundle, attached to a Kronecker h-regular multi-time Lagrangian with partial derivatives of order one.