On the structure of Finsler and areal spaces

TL;DR

This paper explores the geometric structures underlying integral variational functionals related to Finsler and areal geometries, providing insights into their foundational properties and potential extensions to higher-order functionals.

Contribution

It introduces a detailed analysis of the geometric structures for variational functionals in Finsler and areal geometries, highlighting their foundational aspects and extension possibilities.

Findings

Identification of geometric structures for Finsler and areal variational functionals

Extension framework for higher-order variational functionals

Application of Hilbert 1-form in geometric analysis

Abstract

We study underlying geometric structures for integral variational functionals, depending on submanifolds of a given manifold. Applications include (first order) variational functionals of Finsler and areal geometries with integrand the Hilbert 1-form, and admit immediate extensions to higher-order functionals.