Isoparametric hypersurfaces and hypersurfaces with constant principal curvatures in Finsler spaces
Volume 131 / 2023
Annales Polonici Mathematici 131 (2023), 127-140
MSC: Primary 53C60; Secondary 53B40.
DOI: 10.4064/ap230211-15-8
Published online: 20 November 2023
Abstract
We study the relationship between isoparametric hypersurfaces and hypersurfaces with constant principal curvatures in non-Riemannian Finsler spaces. We give some examples of isoparametric hypersurfaces with (non)constant principal curvatures on Randers manifolds with nonconstant flag curvatures. Furthermore, we construct an example of a conformally flat Randers manifold which admits a family of nonisoparametric hyperplanes with constant principal curvatures.
