Integral geometry in Euclidean and projective quaternionic spaces
type: Item
instance of: scholarly article
zbMATH Open document ID: 0989.53048
publication date: 2002-01-13T00:00:00Z
Mathematics Subject Classification ID: 53C65
Mathematics Subject Classification ID: 53C26
zbMATH DE Number: 1689546
zbMATH Keywords: submanifolds
zbMATH Keywords: volume of manifolds
zbMATH Keywords: Lipschitz-Killing curvature
MaRDI profile type: Publication
author: X. Gual
author: A. M. Naveira
author: A. Tarrio
title: Integral geometry in Euclidean and projective quaternionic spaces
published in: Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie. Nouvelle Série
review text: Let \(M\) be a real compact submanifold in an \(n\)-dimensional quaternionic space \(Q^n\). The authors extend a classical result in integral geometry obtaining the volume \(M\) from its intersections with a set of \(r\)-dimensional quaternionic subspaces in \(Q^n\). Next they define the total absolute curvature of a compact quaternionic submanifold \(M\) of the projective quaternionic space \(QP^n\) and relate this curvature with the classical Lipschitz-Killing curvature.
reviewed by: Vasile Oproiu
description: scientific article; zbMATH DE number 1689546