The fundamental equations of conformal submersions
type: Item
instance of: scholarly article
title: The fundamental equations of conformal submersions
zbMATH Open document ID: 0804.53044
author: Liviu Ornea
author: Giuliano Romani
published in: Beiträge zur Algebra und Geometrie
publication date: 1995-01-12T00:00:00Z
full work available at URL: https://eudml.org/doc/229201
full work available at URL: no.2
review text: The authors establish an analogy with the equations of O'Neill for Riemannian submersions. The method consists in attaching to each class of conformal submersions a unique Riemannian submersion, then applying appropriate projectors, taking the conformal invariant components of its fundamental equations. The method was previously used by the same authors for conformal immersions [``Conformal geometry of Riemannian submanifolds. I. Gauss equation; II. Codazzi and Ricci equations'' (Prepr. Univ. degli Studi di Roma (1992)]. After a brief introduction, in the second section the O'Neill equations for Riemannian submersions are rewritten in a slightly modified form. The algebraic preparation (decomposition of algebraic curvature tensors, conformal projectors), is made in section three. Section four introduces the two fundamental (1,2) tensors of a conformal submersion and shows that they practically determine it. In the final sections the five fundamental equations are derived. Conformal submersions are closely related to harmonic morphisms. Using different methods, \textit{S. Gudmundsson} found independently equations of this type [Ph. D. Thesis, University of Leeds (1992)] but in a different form.
Mathematics Subject Classification ID: 53C12
zbMATH DE Number: 510044
zbMATH Keywords: Weyl tensor
zbMATH Keywords: Riemannian submersions
zbMATH Keywords: conformal submersions
zbMATH Keywords: algebraic curvature tensors
zbMATH Keywords: conformal projectors
zbMATH Keywords: harmonic morphisms
reviewed by: S. Ianuş
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 510044