Complex forms on supermanifolds
type: Item
instance of: scholarly article
title: Complex forms on supermanifolds
zbMATH Open document ID: 0654.58006
DOI: 10.1007/BF01077270
publication date: 1986-01-01T00:00:00Z
review text: The authors introduce the notions \(r| s\) forms and an operation ``d'' on the domain of a supermanifold. The main results are: Theorem 1. The operation d is defined invariantly, carries forms of type \(r| s\) into forms of type \((r+1)| s\), and is a differential: \(d^ 2=0\). In the even case the differential constructed coincides with the differential d for exterior forms. Theorem 2. For the differential d constructed for \(r| s\) the Poincaré lemma holds, i.e., any closed form is locally exact.
Mathematics Subject Classification ID: 58A50
Mathematics Subject Classification ID: 58C50
zbMATH DE Number: 4067898
zbMATH Keywords: r\(| s\) forms
zbMATH Keywords: supermanifold
zbMATH Keywords: exterior forms
zbMATH Keywords: Poincaré lemma
author: F. F. Voronov
author: Anton Zorich
reviewed by: Vasil G. Angelov
MaRDI profile type: Publication
cites work: Q3697706
full work available at URL: https://doi.org/10.1007/bf01077270
OpenAlex ID: W2068885359
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 4067898