Bi-symphonic maps between Riemannian manifolds

TL;DR

This paper extends the concept of symphonic maps between Riemannian manifolds by exploring variations in the bi-energy functional related to the pullback metric, contributing to the theoretical understanding of such maps.

Contribution

It introduces a new extension to symphonic maps by analyzing bi-energy functional variations, advancing the theoretical framework in differential geometry.

Findings

Defined bi-symphonic maps as an extension of symphonic maps.

Analyzed variations of the bi-energy functional.

Provided theoretical properties of bi-symphonic maps.

Abstract

This note introduces an extension to the definition of symphonic maps, denoted as $\varphi:(M,g)\longrightarrow(N,h)$, by exploring variations in the bi-energy functional associated with the pullback metric $\varphi^*h$ between two Riemannian manifolds.