Classification of hypersurfaces with parallel Möbius second fundamental form in S n+1.

Let M ⁿ( n ≥ 2) be an immersed umbilic-free hypersurface in the ( n+1)-dimensional unit sphere S ⁿ⁺¹. Then M ⁿ is associated with a so-called Möbius metric g, and a Möbius second fundamental form B which are invariants of M ⁿunder the Möbius transformation group of S ⁿ⁺¹. In this paper, we classify all umbilic-free hypersurfaces with parallel Möbius second fundamental form. [ABSTRACT FROM AUTHOR]