Minimal submanifolds in \(\mathbb{S}^{p-3}\) with constant scalar curvature
type: Item
instance of: scholarly article
title: Minimal submanifolds in \(\mathbb{S}^{p-3}\) with constant scalar curvature
zbMATH Open document ID: 1086.53082
DOI: 10.1007/BF03322863
author: Luiz Amâncio M. jun. Souza
author: Sebastião Carneiro de Almeida
author: Aldir jun. Brasil
published in: Results in Mathematics
publication date: 2005-02-11T00:00:00Z
review text: Let \(S^n\) denote an \(n\)-dimensional unit sphere. In this paper, the authors prove: Theorem 1: Let \(M\subset S^{3+p}\), \(p\geq 1\), be a closed 3-dimensional minimal submanifold with a flat normal bundle and constant scalar curvature \(R\geq 0\). Then \(R= 0\), \(R=3\) or \(R=6\). Theorem 2: Let \(x:M\to S^{3+p}\) be a substantial isometric immersion. Suppose in addition that \(M\) is a closed 3-dimensional minimal submanifold with a flat normal bundle and constant scalar curvature \(R\leq 0\). Then \(p\leq 2\) and \(M\) is (a) an equatorial 3-sphere \(S^3\), (b) a Clifford torus \(S^1(\sqrt 3/3)\times S(\sqrt 6/3)\), (c) a minimal hypersurface of Cartan type, or (d) a product of sphere \(S^1(\sqrt 3/3)\times S^1(\sqrt 3/3) \times S^1(\sqrt 3/3)\).
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 2133429
zbMATH Keywords: minimal submanifold
zbMATH Keywords: scalar curvature
reviewed by: Huafei Sun
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf03322863
OpenAlex ID: W2080629126
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description: scientific article; zbMATH DE number 2133429