Hypersurfaces With Parallel Moebius Ricci Curvature And Vanishing Moebius Form In The Unit Sphere

x : Mⁿ→Sⁿ⁺¹ is a hypersurface without umbilic point in the unit sphere Sⁿ⁺¹ of dimension n + 1. There are four basic invariants of Mⁿ under the Mobius transformation group of Sⁿ⁺¹, they are M|¨bius metric g, M|¨bius second fundamental form B, Mobius form C, Blaschke tensor A. The Ricci curvature Q induced by g is called the M'dbius Ricci curvature of x. In this paper, we give a classification of the hypersurfaces with parallel Mobius Ricci curvature and vanishing Mobius form in Sⁿ⁺¹. Particularly, we give a definite presentation of the Einstein hypersurfaces with vanishing Mobius form in Sⁿ⁺¹.