Some applications of Cartan's theory on three-dimensional Cauchy-Riemann geometry
type: Item
instance of: scholarly article
title: Some applications of Cartan's theory on three-dimensional Cauchy-Riemann geometry
zbMATH Open document ID: 0823.32008
DOI: 10.1007/BF02571921
author: Jih-Hsin Cheng
published in: Mathematische Zeitschrift
publication date: 1995-11-13T00:00:00Z
full work available at URL: https://eudml.org/doc/174746
review text: In part I, we show that in \(\mathbb{C}^ 2\), every nondegenerate real hypersurface with hermitian shape operator is, in fact, locally \(CR\)- equivalent to the unit sphere. In part II, surface area elements invariant under ambient \(CR\) transformations are constructed. Also an invariant Lorentzian metric on the surface is obtained. We deduce the equation of minimal surfaces with respect to the simplest invariant area element. Besides, we also carry out the actual computation for surfaces in the Heisenberg group.
reviewed by: Jih-Hsin Cheng
Mathematics Subject Classification ID: 32V05
Mathematics Subject Classification ID: 53C50
zbMATH DE Number: 784087
zbMATH Keywords: Cartan's theory
zbMATH Keywords: spherical real hypersurface
zbMATH Keywords: invariant Lorentzian metric
zbMATH Keywords: minimal surfaces
zbMATH Keywords: invariant area
MaRDI profile type: Publication
cites work: Sur la géométrie pseudo-conforme des hypersurfaces de l'espace de deux variables complexes
cites work: Real hypersurfaces in complex manifolds
description: scientific article; zbMATH DE number 784087