Comptes Rendus
Differential Geometry
Closed hypersurfaces of S4(1) with constant mean curvature and zero Gauß–Kronecker curvature
Comptes Rendus. Mathématique, Volume 340 (2005) no. 6, pp. 437-440.

We consider a closed hypersurface M3S4(1) with identically zero Gauß–Kronecker curvature. We prove that if M3 has constant mean curvature H, then M3 is minimal, i.e., H=0. This result extends Ramanathan's classification (Math. Z. 205 (1990) 645–658) result of closed minimal hypersurfaces of S4(1) with vanishing Gauß–Kronecker curvature.

Nous considérons une hypersurface fermée (compacte et sans bord) M3S4(1) à courbure de Gauß–Kronecker identiquement nulle. Nous prouvons que si la courbure moyenne H de M3 est constante, alors l'hypersurface M3 est necéssairement minimale, c.à.d, H=0. Ce résultat généralise celui obtenu dans l'article de Ramanathan (Math. Z. 205 (1990) 645–658) concernant les hypersurfaces fermées minimales à courbure de Gauß–Kronecker identiquement nulle dans S4(1).

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2005.01.005

Tsasa Lusala 1; André Gomes de Oliveira 1

1 Instituto de Matemática e Estatística (IME), Universidade de São Paulo (USP), Rua do Matão, 1010, Cidade Universitária, CEP 05508-090 São Paulo – SP, Brazil
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Tsasa Lusala; André Gomes de Oliveira. Closed hypersurfaces of $ {\mathbb{S}}^{4}(1)$ with constant mean curvature and zero Gauß–Kronecker curvature. Comptes Rendus. Mathématique, Volume 340 (2005) no. 6, pp. 437-440. doi : 10.1016/j.crma.2005.01.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.01.005/

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