Abstract
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.
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Li, X.X., Zhang, F.Y. Immersed Hypersurfaces in the Unit Sphere S m+1 with Constant Blaschke Eigenvalues. Acta Math Sinica 23, 533–548 (2007). https://doi.org/10.1007/s10114-005-0919-4
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DOI: https://doi.org/10.1007/s10114-005-0919-4