Immersed Hypersurfaces in the Unit Sphere S m+1 with Constant Blaschke Eigenvalues

For an immersed submanifold x: M m . S n in the unit sphere S n without umbilics, an eigenvalue of the Blaschke tensor of x is called a Blaschke eigenvalue of x. It is interesting to determine all hypersurfaces in S n with constant Blaschke eigenvalues. In this paper, we are able to classify all immersed hypersurfaces in S m+1 with vanishing Möbius form and constant Blaschke eigenvalues, in case (1) x has exact two distinct Blaschke eigenvalues, or (2) m = 3. With these classifications, some interesting examples are also presented