Biharmonic properties and conformal changes
A. Balmus
TL;DR
This paper introduces a new class of biharmonic maps created by conformally deforming the codomain metric of harmonic Riemannian submersions, making them biharmonic but not harmonic.
Contribution
It presents a novel method to generate biharmonic maps through conformal deformation of the target metric of harmonic submersions.
Findings
Constructed new biharmonic maps via conformal deformation
Demonstrated these maps are nonharmonic but biharmonic
Expanded understanding of biharmonic map generation methods
Abstract
We construct a new class of biharmonic maps, which are the critical points for the bienergy functional, by deforming conformally the codomain metric of harmonic Riemannian submersions such that they become nonharmonic but biharmonic.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Analytic and geometric function theory · Point processes and geometric inequalities