Almost complex and complex structures on real projective Stiefel manifolds
type: Item
instance of: scholarly article
title: Almost complex and complex structures on real projective Stiefel manifolds
zbMATH Open document ID: 0944.57021
DOI: 10.1007/BF02844374
author: Július Korbaš
author: Parameswaran Sankaran
publication date: 2000-09-20T00:00:00Z
review text: The projective Stiefel manifold \(X_{n,r}\) is the quotient of the Stiefel manifold \(V_{n,r}\) of orthonormal \(r\)-frames in \(\mathbb{R}^n\) by the \(\mathbb{Z}/2\) action induced from the antipodal action on \(\mathbb{R}^n\). The main result of the paper is the following Theorem. The manifold \(X_{n,r}\) admits an almost complex structure (compatible with the usual differentiable structure) if and only if \(n\) is arbitrary and \(r\equiv 0\pmod 4\) or \(n\) is even and \(r\equiv 3\pmod 4\). It is shown that in fact the manifolds \(X_{n,r}\) of the first type \((r\equiv 0\pmod 4)\) admit complex structures. This is unknown for general manifolds \(X_{n,r}\) of the second type \((r\equiv 3\pmod 4)\).
Mathematics Subject Classification ID: 57R15
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 1279146
zbMATH Keywords: Stiefel manifold
zbMATH Keywords: almost complex structure
reviewed by: Alexander Dranishnikov
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02844374
OpenAlex ID: W2079210144
published in: Rendiconti del Circolo Matematico di Palermo
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description: scientific article; zbMATH DE number 1279146