On hypersurfaces with parallel Möbius form and constant para-Blaschke eigenvalues

Authors : Shujie ZHAI, Xiuli GUO, Zejun HU

Pages : 1180-1191

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :In this paper, we classify umbilic-free hypersurfaces of the unit sphere that have constant para-Blaschke eigenvalues and possess parallel Möbius form. To achieve the classification, we first of all show that, under the condition of having constant para-Blaschke eigenvalues, an umbilic-free hypersurface of the unit sphere is of parallel Möbius form if and only if its Möbius form vanishes identically.
Keywords : Blaschke tensor, Möbius form, Möbius second fundamental form, Möbius metric, parallel Möbius form