An observation about conformal points on surfaces

TL;DR

This paper investigates the existence of special points on surfaces where a symmetric bilinear tensor aligns conformally with a Riemannian metric, with applications to surface diffeomorphisms and vector fields.

Contribution

It introduces new results on the existence of conformal points on surfaces and applies these findings to the study of surface diffeomorphisms and vector fields.

Findings

Existence of conformal points on compact oriented surfaces.

Applications to conformal points of surface diffeomorphisms.

Applications to conformal points of vector fields.

Abstract

We study the existence of points on a compact oriented surface at which a symmetric bilinear two-tensor field is conformal to a Riemannian metric. We give applications to the existence of conformal points of surface diffeomorphisms and vector fields.