Bochner-Simons formulas and the rigidity of biharmonic submanifolds
Dorel Fetcu, Eric Loubeau, Cezar Oniciuc
TL;DR
This paper develops integral formulas of Simons and Bochner type to analyze biharmonic submanifolds in space forms, leading to rigidity results that address key conjectures in the field.
Contribution
It introduces new integral formulas and applies them to prove rigidity results for biharmonic submanifolds, advancing understanding of their geometric properties.
Findings
Rigidity results for biharmonic submanifolds in space forms.
Partial solutions to well-known conjectures in the sphere case.
Development of integral formulas of Simons and Bochner type.
Abstract
We find some integral formulas of Simons and Bochner type and use them to study biharmonic and biconservative submanifolds in space forms. We obtain rigidity results that in the biharmonic case represent partial answers to two well-known conjectures on such submanifolds in spheres.
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