Pinching theorems for totally real minimal submanifolds of \(CP^ n(c)\)
type: Item
instance of: scholarly article
title: Pinching theorems for totally real minimal submanifolds of \(CP^ n(c)\)
zbMATH Open document ID: 0662.53047
author: Hillel Gauchman
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1989-01-01T00:00:00Z
review text: Let h be the second fundamental form of a compact minimal totally real submanifold M of a complex space form \({\mathbb{C}}P^ n(c)\) of holomorphic curvature c. For any \(u\in TM\), set \(\delta (u)=\| h(u,u)\|^ 2.\) It is proved that if \(\delta\) (u)\(\leq c/12\) for any unit vector \(u\in TM\), then either \(\delta\) (u)\(\equiv 0\) (i.e. M is totally geodesic) or \(\delta\) (u)\(\equiv c/12\). All compact minimal totally real submanifolds of \({\mathbb{C}}P^ n(c)\) satisfying \(\delta\) (u)\(\equiv c/12\) are determined.
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 4082451
zbMATH Keywords: pinching theorem
zbMATH Keywords: minimal totally real submanifold
zbMATH Keywords: complex space form
zbMATH Keywords: totally geodesic
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178227823
OpenAlex ID: W1978050969
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DOI: 10.2748/TMJ/1178227823
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description: scientific article; zbMATH DE number 4082451