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A short proof of the homogeneity of an isoparametric hypersurface with
Chao Qian, Zizhou Tang
A well-known hypersurface classification theorem states that any isoparametric hypersurface in with six principal curvatures is homogeneous. This landmark result was first…
Isoparametric foliations and complex structures
Chao Qian, Zizhou Tang, Wenjiao Yan
Explicit representations of complex structures on closed manifolds are valuable, but relatively rare in the literature. Using isoparametric theory, we construct complex structures…
On two questions of James
Chao Qian, Zizhou Tang, Wenjiao Yan
64 years ago, I. M. James raised two fundamental questions about octonionic Stiefel spaces. The prime objective of this paper is to figure out partial answers to both of them.
Extrinsic geometry of the Gromoll-Meyer sphere
Chao Qian, Zizhou Tang, Wenjiao Yan
Among a family of 2-parameter left invariant metrics on Sp(2), we determine which have nonnegative sectional curvatures and which are Einstein. On the quotiente $\widetilde{N}^{11}…
Clifford algebra, isoparametric foliation and related geometric constructions
Chao Qian, Zizhou Tang
Based on representation theory of Clifford algebra, Ferus, Karcher and Münzner constructed a series of isoparametric foliations. In this paper, we will survey recent studies on iso…