Covariant symplectic geometry of binary forms and singularities of systems of rays
type: Item
instance of: scholarly article
title: Covariant symplectic geometry of binary forms and singularities of systems of rays
zbMATH Open document ID: 0787.53026
DOI: 10.1016/0034-4877(92)90010-X
published in: Reports on Mathematical Physics
publication date: 1994-05-09T00:00:00Z
review text: The author generalizes the method for classifying the polynomial covariants of binary forms by using umbral calculus to obtain a general framework to describe the tensor invariants and the corresponding invariant subspaces of binary forms. As a consequence he obtains the unique invariant symplectic structure and Riemannian structure on the spaces of binary forms of odd and, respectively, even degree. In addition, the unique invariant contact structure on this space is found. Finally, by using the theory of common covariants of binary forms, the hierarchy of apolar coisotropic manifolds and generalized open swallowtails is derived.
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 05A30
Mathematics Subject Classification ID: 15A72
zbMATH DE Number: 465505
zbMATH Keywords: polynomial covariants
zbMATH Keywords: tensor invariants
zbMATH Keywords: contact structure
zbMATH Keywords: apolar coisotropic manifolds
zbMATH Keywords: generalized open swallowtails
author: Stanisław Janeczko
reviewed by: Neculai Papaghiuc
MaRDI profile type: Publication
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full work available at URL: 0034-4877(92)90010-x
OpenAlex ID: W2141683008
description: scientific article; zbMATH DE number 465505