Geometric structures as variational objects, I

TL;DR

This paper offers a variational framework to describe fundamental differential geometric structures on smooth manifolds, providing a new perspective on their mathematical formulation.

Contribution

It introduces a variational approach to characterize basic geometric structures, bridging differential geometry with variational methods.

Findings

Unified variational description of geometric structures

Potential applications in geometric analysis and physics

Foundational insights into geometric variational principles

Abstract

This note provides a variational description of the most basic differential geometric structures on a smooth manifold.