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Bochner–Simons Formulas and the Rigidity of Biharmonic Submanifolds

Abstract

New integral formulas of Simons and Bochner type are found and then used to study biharmonic and biconservative submanifolds in space forms. This leads to new rigidity results and partial answers to conjectures on biharmonic submanifolds in spheres.

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Acknowledgements

Thanks are due to the referees for valuable comments and suggestions.

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Correspondence to Dorel Fetcu.

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This work was supported by a grant of the Romanian Ministry of Research and Innovation, CCCDI-UEFISCDI, project number PN-III-P3.1-PM-RO-FR-2019-0234/1BM/2019, within PNCDI III, and the PHC Brancusi 2019 project no 43460 TL.

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Fetcu, D., Loubeau, E. & Oniciuc, C. Bochner–Simons Formulas and the Rigidity of Biharmonic Submanifolds. J Geom Anal 31, 1732–1755 (2021). https://doi.org/10.1007/s12220-019-00323-y

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Keywords

  • Stress-energy tensor
  • Constant mean curvature hypersurfaces
  • Biharmonic submanifolds
  • Biconservative submanifolds
  • Real space forms

Mathematics Subject Classification

  • 53C42
  • 53C24
  • 53C21