Geometry of Distributions and $F-$Gordon equation
Mehdi Nadjafikhah, Reza Aghayan
TL;DR
This paper explores the geometric structure of distributions through symmetries, provides a simplified proof of Frobenius theorem, and investigates the geometry of solutions to the F-Gordon equation in differential geometry and physics.
Contribution
It offers a new geometric perspective on distributions, simplifies foundational theorems, and analyzes the solutions of the F-Gordon equation in a unified framework.
Findings
Symmetries characterize the geometry of distributions.
A simplified proof of Frobenius theorem is presented.
Geometric analysis of F-Gordon equation solutions.
Abstract
In this paper we describe the geometry of distributions by their symmetries, and present a simplified proof of the Frobenius theorem and some related corollaries. Then, we study the geometry of solutions of Gordon equation; A PDE which appears in differential geometry and relativistic field theory.
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Taxonomy
TopicsMathematical and Theoretical Analysis