Preprint 677-2000

Tchebychev surfaces of S^3(1) with constant curvature functions

Author(s) : Tsasa Lusala

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 677-2000

MSC 2000

53B25 Local submanifolds

53A15 Affine differential geometry

Abstract :
We prove that Tchebychev surfaces of $\mathbb{S}^3(1)$ with constant mean curvature or with shape operator of constant squared length are isoparametric. We summarize our results in a survey of types of isoparametric and non-isoparametric Tchebychev surfaces.

Keywords : Tchebychev surfaces in S^3(1), locally symmetric surfaces, isoparametric surfaces