On a class of mappings between Riemannian manifolds

TL;DR

This paper explores a class of mappings between Riemannian manifolds influenced by geometric constraints, using an elliptic-hyperbolic generalization of harmonic map equations, and provides conditions for their triviality.

Contribution

It introduces a generalized elliptic-hyperbolic framework for mappings between Riemannian manifolds and establishes conditions under which these mappings are globally trivial.

Findings

Conditions for global triviality of mappings

Extension of harmonic map equations to elliptic-hyperbolic form

Application to steady flow potentials in geometry

Abstract

Effects of geometric constraints on a steady flow potential are described by an elliptic-hyperbolic generalization of the harmonic map equations. Sufficient conditions are given for global triviality.