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Bochner–Simons Formulas and the Rigidity of Biharmonic Submanifolds

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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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Authors and Affiliations

  1. Department of Mathematics and Informatics, Gh. Asachi Technical University of Iasi, Bd. Carol I, 11, 700506, Iasi, Romania

    Dorel Fetcu

  2. Univ. Brest, CNRS UMR 6205, LMBA, 29238, Brest, France

    Eric Loubeau

  3. Faculty of Mathematics, Al. I. Cuza University of Iasi, Bd. Carol I, 11, 700506, Iasi, Romania

    Cezar Oniciuc

Authors
  1. Dorel Fetcu
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  2. Eric Loubeau
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  3. Cezar Oniciuc
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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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  • DOI: https://doi.org/10.1007/s12220-019-00323-y

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