Tchebychev surfaces of \(\mathbb{S}^3(1)\) with constant curvature functions
type: Item
instance of: scholarly article
title: Tchebychev surfaces of \(\mathbb{S}^3(1)\) with constant curvature functions
zbMATH Open document ID: 0964.53013
DOI: 10.1007/BF03322436
author: Tsasa Lusala
published in: Results in Mathematics
publication date: 2000-08-31T00:00:00Z
review text: A hypersurface in a space form is called nondegenerate if its Weingarten operator has maximal rank. Denote by \(\nabla\)(I), \(\nabla\)(II), \(\nabla\)(III) the Levi-Civita connections associated to the three fundamental forms I, II, III, resp., and by \(2C\) the symmetric \((1,2)\)-tensor \(\nabla\)(I)--\(\nabla\)(III). Its traceless part \(\widetilde C\) is an interesting geometric object, it has properties analogous to that of the cubic form in affine hypersurface theory. The author introduces a new class of interesting hypersurfaces, called Tchebychev hypersurfaces, characterized by the property that the covariant derivative \(\nabla\)(II)\(\widetilde C\) is totally symmetric. The author classifies Tchebychev surfaces in the 3-sphere \(\mathbb{S}^3(1)\) with particular curvature properties.
reviewed by: Udo Simon
Mathematics Subject Classification ID: 53B25
Mathematics Subject Classification ID: 53A15
zbMATH DE Number: 1498583
zbMATH Keywords: cyclide
zbMATH Keywords: quadric
zbMATH Keywords: higher-order Codazzi tensor
zbMATH Keywords: cubic form
zbMATH Keywords: Tchebychev hypersurface
MaRDI profile type: Publication
cites work: Q4839161
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full work available at URL: https://doi.org/10.1007/bf03322436
OpenAlex ID: W2083106143
description: scientific article; zbMATH DE number 1498583