Scalar curvature and real submanifolds of codimension 2 of a complex projective space
type: Item
instance of: scholarly article
title: Scalar curvature and real submanifolds of codimension 2 of a complex projective space
zbMATH Open document ID: 0563.53045
DOI: 10.1007/BF01164027
author: Masafumi Okumura
published in: Mathematische Zeitschrift
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173668
review text: One of the main problems concerning real submanifolds of a complex manifold is to give nice conditions for the submanifold to be a complex submanifold. In the case that the ambient manifold is a complex projective space H. B. Lawson gave a condition for an even-dimensional real minimal submanifold to be not only a complex submanifold but also a totally geodesic complex linear subspace. The condition is given by an inequality between the scalar curvature of the submanifold and that of the ambient manifold. In this paper we study real submanifolds of codimension 2 that are not necessarily minimal and prove that under a suitable condition on the normal connection, if the scalar curvature of the submanifold is not smaller than that of a standard complex linar subspace, then the submanifold is necessarily a totally geodesic complex linear subspace.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 3897777
zbMATH Keywords: complex projective space
zbMATH Keywords: real submanifolds
zbMATH Keywords: codimension 2
zbMATH Keywords: normal connection
zbMATH Keywords: scalar curvature
zbMATH Keywords: totally geodesic
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3897777