Conformal Riemannian morphisms between Riemannian manifolds

TL;DR

This paper introduces conformal Riemannian morphisms, a broad class of maps between Riemannian manifolds that generalize many classical concepts like isometries and submersions, and characterizes their properties.

Contribution

It defines conformal Riemannian morphisms and establishes their fundamental properties, including conditions under which they are immersions, submersions, or conformal maps.

Findings

Injective conformal Riemannian morphisms are conformal immersions.

Surjective conformal Riemannian morphisms are conformal submersions.

Bijective conformal Riemannian morphisms are conformal maps.

Abstract

In this article we introduce conformal Riemannian morphisms. The idea of conformal Riemannian morphism generalizes the notions of an isometric immersion, a Riemannian submersion, an isometry, a Riemannian map and a conformal Riemannian map. We show that every injective conformal Riemannian morphism is an injective conformal immersion, and that on a connected manifold, every surjective conformal Riemannian morphism is a surjective conformal submersion, and every bijective conformal Riemannian morphism is a conformal map.