Biharmonic and biconservative hypersurfaces in space forms
Dorel Fetcu, Cezar Oniciuc
TL;DR
This paper reviews properties of biharmonic and biconservative hypersurfaces in space forms, introduces a new perspective on classical results by replacing constant mean curvature with biconservativity, and surveys recent advances.
Contribution
It offers a comprehensive survey of biharmonic and biconservative hypersurfaces and proposes an alternative approach to a classical theorem using biconservativity.
Findings
Summary of general properties of biharmonic and biconservative submanifolds
New formulation of classical results replacing CMC with biconservativity
Insights into the structure of hypersurfaces in space forms
Abstract
We present some general properties of biharmonic and biconservative submanifolds and then survey recent results on such hypersurfaces in space forms. We also propose an alternative version for a well-known result of Nomizu and Smyth for hypersurfaces by replacing the CMC hypothesis with the more general condition of biconservativity.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Geometric and Algebraic Topology