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An Observation About Conformal Points on Surfaces

An Observation About Conformal Points on Surfaces
Ellipsoid with lines of curvature and umbilical points (red). Attribution: Ag2gaeh, CC BY-SA 4.0, via Wikimedia Commons

Peter Albers and Gabriele Benedetti

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.

Arnold Math J. (2024)