Decompositions of para-complex vector bundles and para-complex affine immersions
type: Item
instance of: scholarly article
title: Decompositions of para-complex vector bundles and para-complex affine immersions
zbMATH Open document ID: 1116.53020
DOI: 10.1007/BF03323368
author: Marie-Amélie Lawn
author: Lars Schäfer
published in: Results in Mathematics
publication date: 2007-01-23T00:00:00Z
review text: In this work, decompositions of para-complex and para-holomorphic vector bundles endowed with a connection over a para-complex manifold are studied. At first, the authors investigate connections and morphisms of para-holomorphic vector bundles. In particular, they prove that any connection with vanishing (0,2)-cuvature on a para-complex vector bundle \(E\) induces a unique para-holomorphic structure on \(E\). Then para-holomorphic decompositions are analyzed. Furthermore the authors introduce para-complex affine immersions and investigate decompositions induced by them. Finally, the above results are applied to obtain existence and uniqueness theorems for para-complex affine immersions.
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 53C05
Mathematics Subject Classification ID: 53A15
zbMATH DE Number: 5117898
zbMATH Keywords: para-complex vector bundle
zbMATH Keywords: para-holomorphic vector bundle
zbMATH Keywords: para-complex affine immersion
zbMATH Keywords: para-holomorphic affine immersion
zbMATH Keywords: affine para-Kähler immersion
reviewed by: Valeriy Yumaguzhin
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5117898