Vector fields on real flag manifolds
type: Item
instance of: scholarly article
title: Vector fields on real flag manifolds
zbMATH Open document ID: 0579.57017
DOI: 10.1007/BF01000338
author: Július Korbaš
published in: Annals of Global Analysis and Geometry
publication date: 1985-01-01T00:00:00Z
review text: This paper determines which of the flag manifolds \(F=F(n_ 1,...,n_ r)\) are parallelizable. This is the space of mutually orthogonal r-tuples of subspaces of dimensions \(n_ 1,...,n_ r\) in \({\mathbb{R}}^ n\), \(n=n_ 1+...+n_ r\). It is shown that the parallelizable F's are precisely those given by \(F(1,3)={\mathbb{R}}P^ 3\), \(F(1,7)={\mathbb{R}}P^ 7\), and the classical flag manifolds F(1,1,...,1). Further, the author says a few words about the span of F, the number of linearly independent vector fields. In particular, \(span(F(1,1,2))=3.\) (Note: See \textit{P. Sankaran} and \textit{P. Zvengrowski} [Pac. J. Math. 122, 455-458 (1986; Zbl 0557.14030)] for recent additional work.)
Mathematics Subject Classification ID: 57R15
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 14M15
zbMATH DE Number: 3927926
zbMATH Keywords: flag manifolds
zbMATH Keywords: parallelizable
zbMATH Keywords: number of linearly independent vector fields
MaRDI profile type: Publication
cites work: La cohomologie \(\mod 2\) de certains espaces homogènes
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description: scientific article; zbMATH DE number 3927926