On symplectic submanifolds of cotangent bundles
type: Item
instance of: scholarly article
title: On symplectic submanifolds of cotangent bundles
zbMATH Open document ID: 0801.53022
DOI: 10.1007/BF00750961
author: Mark J. Gotay
published in: Letters in Mathematical Physics
publication date: 1994-03-17T00:00:00Z
review text: Let \(M\) be a differentiable manifold and \(T^* M\) its canonical cotangent bundle equipped with the standard symplectic form. Let \(S\) be a symplectic submanifold of \(T^* M\). The author derives analytic, necessary and sufficient conditions for \(S\) to be the canonical cotangent bundle of a submanifold of \(M\) or, more generally, of a quotient space of a submanifold of \(M\). Next, he discusses several physical examples of his results. Especially, massive scalar particles, fixed-point sets of symplectic group actions, Dirac manifolds for angular momentum, the Proca field.
reviewed by: Zbigniew Olszak
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 70G10
zbMATH DE Number: 508689
zbMATH Keywords: cotangent bundle
zbMATH Keywords: symplectic submanifold
zbMATH Keywords: Dirac manifolds
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00750961
OpenAlex ID: W2155734357
description: scientific article; zbMATH DE number 508689