Biharmonic CMC Hypersurfaces in the Warped Product Space
Najma Mosadegh, Esmaiel Abedi
TL;DR
This paper characterizes proper biharmonic constant mean curvature hypersurfaces in a specific warped product space, establishing conditions for their existence and proving non-existence of compact examples.
Contribution
It provides necessary and sufficient conditions for proper biharmonic CMC hypersurfaces and shows that no compact examples exist in the studied space.
Findings
Derived conditions for proper biharmonic CMC hypersurfaces.
Proved non-existence of proper biharmonic compact hypersurfaces.
Enhanced understanding of biharmonic hypersurfaces in warped product spaces.
Abstract
We find the necessary and sufficient condition for the proper biharmonic CMC hypersurfaces in the special warped product space. Furthermore, we obtain that there exists no proper biharmonic CMC compact hypersurface there.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Geometric and Algebraic Topology