On the submanifolds of an almost para-Hermitian manifold
type: Item
instance of: scholarly article
title: On the submanifolds of an almost para-Hermitian manifold
zbMATH Open document ID: 0955.53030
DOI: 10.1023/A:1006779919681
published in: Acta Mathematica Hungarica
publication date: 2000-11-13T00:00:00Z
review text: An almost para-Hermitian manifold \((\overline M,\overline J, \overline g)\) is a differentiable manifold \(\overline M\) endowed with an almost product structure \(\overline J\), that is, a tensor field \(\overline J\) of type \((1,1)\) obeying \(\overline J\circ\overline J=Id\), and a pseudo-Riemannian metric \(\overline g\) such that \(\overline g(\overline JX,Y)+\overline g(X,\overline JY)=0\), for all vector fields \(X\) and \(Y\). In this paper, the authors give the classification of degenerate and non-degenerate submanifolds, and CR-submanifolds, of an almost para-Hermitian manifold of dimension four. They provide also examples from each class. As a consequence of that classification, the authors find that there exist submanifolds which admit more than one CR-structure, revealing a profound difference between complex and para-complex geometries.
reviewed by: Pascual Lucas Saorín
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 1528628
zbMATH Keywords: CR-submanifold
zbMATH Keywords: para-Hermitian manifold
zbMATH Keywords: hyperbolic Hermite manifold
author: Fernando Etayo
author: Mario Fioravanti
author: Ujué R. Trías
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1528628