\(n\)-dimensional totally real minimal submanifolds of \(CP^ n\)
type: Item
instance of: scholarly article
title: \(n\)-dimensional totally real minimal submanifolds of \(CP^ n\)
zbMATH Open document ID: 0874.53048
author: Domenico Perrone
published in: Archiv der Mathematik
publication date: 1997-07-06T00:00:00Z
review text: \(S_{1,n-1}=S^1(\sin\theta \cos\theta)\times S^{n-1}(\sin\theta)\), \(\tan\theta=\sqrt n\), can be immersed as a totally real minimal submanifold in \(P_n(\mathbb{C})\) with parallel second fundamental form. The author proves that, among all 6-dimensional conformally flat minimal submanifolds in \(P_6(\mathbb{C})\), \(S_{1,5}\) is characterized as the one with positive Euler number and constant scalar curvature \(\tau\), \(0<\tau\leq 70/3\). A similar result was obtained by \textit{N. Ejiri} [Proc. Am. Math. Soc. 86, 496-497 (1982; Zbl 0499.53046)] when \(n=4\). The author also proves that, among all 4-dimensional totally real minimal submanifolds in \(P_4(\mathbb{C})\) with parallel second fundamental form, \(S_{1,3}\) can be characterized as the one with scalar curvature \(\geq 13/2\).
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 1028205
zbMATH Keywords: totally real minimal submanifold
zbMATH Keywords: parallel second fundamental form
zbMATH Keywords: positive Euler number
zbMATH Keywords: constant scalar curvature
reviewed by: Koichi Ogiue
MaRDI profile type: Publication
full work available at URL: s000130050066
OpenAlex ID: W2044643496
cites work: On Totally Real Submanifolds
cites work: Totally Real Minimal Submanifolds in a Complex Projective Space
cites work: Totally Real Minimal Immersions of n-Dimensional Real Space Forms into n-Dimensional Complex Space Forms
cites work: On the Holonomy Group of the Conformally Flat Riemannian Manifold
cites work: Totally real minimal submanifolds in \(CP^ n\)
cites work: Totally real parallel submanifolds in \(P^ n(\)c)
cites work: On eigen-values of Laplacian and curvature of Riemannian manifold
DOI: 10.1007/S000130050066
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description: scientific article; zbMATH DE number 1028205