On the existence of Generalized Unicorns on Surfaces

TL;DR

This paper investigates the existence of generalized Landsberg structures on surfaces by applying the Cartan-Kähler Theorem and a Path Geometry approach, advancing understanding in differential geometry.

Contribution

It introduces a novel application of the Cartan-Kähler Theorem combined with Path Geometry to study generalized Landsberg structures on surfaces.

Findings

Established conditions for existence of generalized Landsberg structures

Applied Cartan-Kähler Theorem to surface geometries

Provided new insights into differential geometric structures

Abstract

This paper addresses the problem of existence of generalized Landsberg structures on surfaces using the Cartan-K\"ahler Theorem and a Path Geometry approach.