On interpolating sesqui-harmonic maps between Riemannian manifolds

TL;DR

This paper introduces a new class of maps called interpolating sesqui-harmonic maps, which generalize harmonic and biharmonic maps, motivated by string theory actions with extrinsic curvature, and explores their mathematical properties.

Contribution

It defines and studies the properties of interpolating sesqui-harmonic maps, bridging harmonic and biharmonic maps within a rigorous mathematical framework.

Findings

Defined the interpolating sesqui-harmonic map functional

Analyzed basic properties of critical points

Established foundational results for this new class of maps

Abstract

Motivated from the action functional for bosonic strings with extrinsic curvature term we introduce an action functional for maps between Riemannian manifolds that interpolates between the actions for harmonic and biharmonic maps. Critical points of this functional will be called interpolating sesqui-harmonic maps. In this article we initiate a rigorous mathematical treatment of this functional and study various basic aspects of its critical points.