Harmonic maps and biharmonic Riemanian submersions
Hajime Urakawa
TL;DR
This paper characterizes when Riemannian submersions are harmonic or biharmonic, providing examples of biharmonic submersions that are not harmonic, thus advancing understanding of their geometric properties.
Contribution
It offers new characterizations for harmonic and biharmonic Riemannian submersions and presents explicit examples of biharmonic submersions that are not harmonic.
Findings
Characterizations for harmonic Riemannian submersions.
Characterizations for biharmonic Riemannian submersions.
Examples of biharmonic but not harmonic submersions.
Abstract
Characterizations for Riemannian submersions to be harmonic or biharmonic are shown. Examples of biharmonic but not harmonic Riemannian submersions are shown.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Dermatological and Skeletal Disorders