Relativgeometrische Kennzeichnungen euklidischer Hypersphären. (Characterizations of Euclidean hyperspheres in relative geometry)
type: Item
instance of: scholarly article
title: Relativgeometrische Kennzeichnungen euklidischer Hypersphären. (Characterizations of Euclidean hyperspheres in relative geometry)
zbMATH Open document ID: 0733.53006
DOI: 10.1007/BF00182120
author: Friedrich Manhart
published in: Geometriae Dedicata
publication date: 1989-01-01T00:00:00Z
review text: The author studies locally strongly convex hypersurfaces of Euclidean n- space. He assumes that a relative normalization is given for them. Extending the geometric calculations initiated by \textit{R. Schneider} [Math. Z. 101, 375-406 (1967; Zbl 0156.201)] he develops integral formulas for the different kinds of curvatures connected with such a normalization and with the second fundamental form. Then, assuming certain inequalities for these curvatures, he uses the integral formulas to derive several interesting local and global geometric characterizations of Euclidean hyperspheres. The results are too complicated to be described here in detail.
Mathematics Subject Classification ID: 53A15
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 4212912
zbMATH Keywords: strongly convex hypersurfaces
zbMATH Keywords: relative normalization
zbMATH Keywords: second fundamental form
zbMATH Keywords: integral formulas
zbMATH Keywords: characterizations of Euclidean hyperspheres
reviewed by: Bernd Wegner
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4212912