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

Authors: SHUJIE ZHAI, XIULI GUO, ZEJUN HU

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

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