Fenchel type theorem for submanifolds of \(S^ n\)
type: Item
instance of: scholarly article
title: Fenchel type theorem for submanifolds of \(S^ n\)
zbMATH Open document ID: 0880.53047
DOI: 10.1007/BF02566438
author: Harold Rosenberg
author: Rémi Langevin
published in: Commentarii Mathematici Helvetici
publication date: 1998-01-12T00:00:00Z
full work available at URL: https://eudml.org/doc/140415
review text: The main result is: Let \(M\) be a compact hypersurface in the \(n\)-dimensional sphere, then \[ \sum^{n-1}_{i=0} c_iL_i (M)\geq \beta (M), \] where \(\beta (M)=\) sum of the Betti numbers of \(M\), \(L_i =i\)-length functional, defined integral-geometrically and localized through absolute curvature terms of \(M\), \(c_i=\) dimension constants. Further results of this nature deal with knotted curves and surfaces in spheres. Remark: Concerning the optimal Fenchel type theorem for curves in spheres cf. [\textit{E. Teufel}, Manuscr. Math. 75, 43-48 (1992; Zbl 0754.53009)].
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C65
zbMATH DE Number: 1008571
zbMATH Keywords: Fenchel type theorem
zbMATH Keywords: submanifolds in spheres
zbMATH Keywords: knotted surfaces
zbMATH Keywords: \(i\)-length functional
reviewed by: Eberhard Teufel
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1008571