26 citations · 46 across the 13 of their papers we have counts for
17 papers
Collapse to nonsmoothable manifolds under lower sectional and positive Ricci curvature bounds
Jian Ge, Chao Qian
We construct smooth collapsing sequences with sectional curvature at least whose limits are topological manifolds with nonzero Kirby--Siebenmann class. For every , the…
On the Bryant conjecture for minimal hypersurfaces in
Chao Qian, Ya Tao
We prove that a local minimal hypersurface in the unit sphere with constant scalar curvature and three distinct principal curvatures at every point must be locally cong…
A concise proof of 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…
Symmetry of hypersurfaces with symmetric boundary
Hui Ma, Chao Qian, Jing Wu +1
Let be a compact connected subgroup of . In , we gain interior -symmetry for minimal hypersurfaces and hypersurfaces of constant mean curvature (C…
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.
Clifford systems, harmonic maps and metrics with non-negative curvature
Chao Qian, Zizhou Tang, Wenjiao Yan
Associated with a symmetric Clifford system on , there is a canonical vector bundle over . For and , we construc…
Topology and curvature of isoparametric families in spheres
Chao Qian, Zizhou Tang, Wenjiao Yan
An isoparametric family in the unit sphere consists of parallel isoparametric hypersurfaces and their two focal submanifolds. The present paper has two parts. The first part invest…
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…
Ricci curvature of double manifolds via isoparametric foliations
ChiaKuei Peng, Chao Qian
Given a closed manifold and a vector bundle of rank over , by gluing two copies of the disc bundle of , we can obtain a closed manifold , the so-called d…
Differential topology interacts with isoparametric foliations
Jianquan Ge, Chao Qian
In this note, we discuss the interactions between differential topology and isoparametric foliations, surveying some recent progress and open problems.
Isoparametric foliations, a problem of Eells-Lemaire and conjectures of Leung
Chao Qian, Zizhou Tang
In this paper, two sequences of minimal isoparametric hypersurfaces are constructed via representations of Clifford algebras. Based on these, we give estimates on eigenvalues of th…
Recent progress in isoparametric functions and isoparametric hypersurfaces
Chao Qian, Zizhou Tang
This paper gives a survey of recent progress in isoparametric functions and isoparametric hypersurfaces, mainly in two directions. (1) Isoparametric functions on Riemannian manifol…
Isoparametric functions on exotic spheres
Chao Qian, Zizhou Tang
This paper extends widely the work in \cite{GT13}. Existence and non-existence results of isoparametric functions on exotic spheres and Eells-Kuiper projective planes are establish…
New examples of Willmore submanifolds in the unit sphere via isoparametric functions,II
Chao Qian, Zizhou Tang, Wenjiao Yan
This paper is a continuation of a paper with the same title of the last two authors. In the first part of the present paper, we give a unified geometric proof that both focal subma…
Finiteness theorems for equifocal hypersurfaces
Jianquan Ge, Chao Qian, Zizhou Tang
In this paper, we give a finiteness result on the diffeomorphism types of curvature-adapted equifocal hypersurfaces in a simply connected compact symmetric space. Furthermore, the…