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Minimal Submanifolds in Sp+3 with Constant Scalar Curvature

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Abstract

Let M be a compact, minimal 3-dimensional submanifold with constant scalar curvature R immersed in the standard sphere S3+p. In codimension 1, we know from the work that has been done on Chern’s conjecture that M is isoparametric and R = 3D0, R = 3D3 or R = 3D6. In this paper we extend this result from codimension one to compact submanifolds with a flat normal bundle and give a complete classification.

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Authors and Affiliations

  1. CAEN, Universidade Federal do Ceará=, Av. da Universidade, 2700 — 2o andar — Benfica, 60020-181, Fortaleza-CE, Brazil

    Sebastiāo C. de Almeida

  2. Departamento de Matemática, Universidade Federal do Ceará, Campus do Pici, 60455-760, Fortaleza-CE, Brazil

    Aldir Brasil Jr.

  3. Departamento de Matemática e Estatstica, Universidade do Rio de Janeiro, Av Pasteur 458, Urca, 22290-240, RIO de Janeiro-RJ, Brazil

    Luiz Amâncio M. Souza Jr.

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  1. Sebastiāo C. de Almeida
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  2. Aldir Brasil Jr.
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  3. Luiz Amâncio M. Souza Jr.
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Correspondence to Sebastiāo C. de Almeida.

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de Almeida, S.C., Brasil, A. & Souza, L.A.M. Minimal Submanifolds in Sp+3 with Constant Scalar Curvature. Results. Math. 46, 1–9 (2004). https://doi.org/10.1007/BF03322863

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  • DOI: https://doi.org/10.1007/BF03322863

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