Hermitean quadrics as contact manifolds
type: Item
instance of: scholarly article
title: Hermitean quadrics as contact manifolds
zbMATH Open document ID: 0555.53020
DOI: 10.1216/RMJ-1984-14-3-559
author: Jay P. Fillmore
published in: Rocky Mountain Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: As it is well known the projective cotangent bundle of real projective space, a real contact manifold, is a real form of the projective cotangent bundle of complex projective space, a complex contact manifold. Hermitean quadrics (which are real manifolds in complex projective space) are real contact manifolds and are also real forms of the projective cotangent bundle of complex projective space. The latter is not evident and it is the purpose of the present paper to establish these assertions, exhibit their connection with the anti-polarities of classical projective geometry, and to show that these two types of real contact manifolds constitute all of the real forms of the projective cotangent bundle of complex projective space, as homogeneous contact manifolds. The development to these facts leads to the remark that Hermitean quadrics are principal circle bundles over products of complex projective spaces and generalize the Hopf bundle as real contact manifolds.
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 32M10
zbMATH DE Number: 3884904
zbMATH Keywords: cotangent bundle
zbMATH Keywords: projective space
zbMATH Keywords: contact manifold
zbMATH Keywords: Hermitean quadrics
zbMATH Keywords: circle bundles
reviewed by: Radu Iordănescu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3884904