Biharmonic Hypersurfaces in 4-Dimensional Space Forms
A. Balmu\c{s}, S. Montaldo, and C. Oniciuc
TL;DR
This paper classifies all proper biharmonic hypersurfaces with up to three principal curvatures in 4-dimensional space forms, providing a complete understanding of their geometric structure.
Contribution
It offers the first full classification of proper biharmonic hypersurfaces in 4-dimensional space forms, expanding the understanding of biharmonic submanifolds.
Findings
Complete classification of proper biharmonic hypersurfaces in 4D space forms
Identification of hypersurfaces with up to three principal curvatures
Advancement in understanding biharmonic geometry in higher dimensions
Abstract
We investigate proper biharmonic hypersurfaces with at most three distinct principal curvatures in space forms. We obtain the full classification of proper biharmonic hypersurfaces in 4-dimensional space forms.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Mathematics and Applications