26 citations · 61 across the 21 of their papers we have counts for
23 papers
A Complex Structure on : The Genus-One Case of Calabi's Problem
Min Gao, Zizhou Tang, Wenjiao Yan
We construct a complex structure on , giving an affirmative answer to the genus-one case of Calabi's problem. The resulting compact complex threefold is non-Kähler a…
Chern's Conjecture with Constant Cubic Trace
Huixin Tan, Zizhou Tang, Yuquan Xie +1
We prove that the values set of \(S=|A|^2\) attained by closed embedded minimal hypersurfaces in \(\mathbb S^{n+1}(1)\) with constant \(S\) and constant \(f_3=\operatorname{tr}(A^3…
Rigidity of Closed Minimal Hypersurfaces in
Jianquan Ge, Tong Liu, Keyan Luo +1
The celebrated Chern conjecture asserts that any closed minimal hypersurface in with constant scalar curvature is isoparametric. In this paper, we resolve this c…
Non-extendability of complex structures
Zizhou Tang, Wenjiao Yan
There exists a complex structure on a connected open subset of . The present paper proves that: (1) can be extended to a global almost complex struct…
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…
Orthogonal almost complex structure and its Nijenhuis tensor
Zizhou Tang, Wenjiao Yan
In this paper, we demonstrate that on an almost Hermitian manifold , a 2-form , the pulling back of the Kähler form on the twistor bundle over $M^{2n…
Isoparametric hypersurfaces and complex structures
Zizhou Tang, Wenjiao Yan
The main purpose of this note is to construct almost complex or complex structures on certain isoparametric hypersurfaces in unit spheres. As a consequence, complex structures on $…
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…
On the Chern conjecture for isoparametric hypersurfaces
Zizhou Tang, Wenjiao Yan
For a closed hypersurface with constant mean curvature and constant non-negative scalar curvature, the present paper shows that if $\mathrm{tr}(\mathcal{A}^…
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}…
A sufficient condition for a hypersurface to be isoparametric
Zizhou Tang, Dongyi Wei, Wenjiao Yan
Let be a closed Riemannian manifold on which the integral of the scalar curvature is nonnegative. Suppose is a symmetric tensor field whose dual $(1,1)…
Isoparametric theory and its applications
Zizhou Tang, Wenjiao Yan
This is a survey on the recent progress in several applications of isoparametric theory, including an affirmative answer to Yau's conjecture on the first eigenvalue of Laplacian in…
Normal scalar curvature inequality on the focal submanifolds of isoparametric hypersurfaces
Jianquan Ge, Zizhou Tang, Wenjiao Yan
An isoparametric hypersurface in unit spheres has two focal submanifolds. Condition A plays a crucial role in the classification theory of isoparametric hypersurfaces in [CCJ07], […
Isoparametric foliation and a problem of Besse on generalizations of Einstein condition
Zizhou Tang, Wenjiao Yan
The focal sets of isoparametric hypersurfaces in spheres with g = 4 are all Willmore submanifolds, being minimal but mostly non-Einstein ([TY1], [QTY]). Inspired by A.Gray's view,…
Isoparametric foliation and Yau conjecture on the first eigenvalue, II
Zizhou Tang, Yuquan Xie, Wenjiao Yan
This is a continuation of Tang and Yan, which investigated the first eigenvalues of minimal isoparametric hypersurfaces with distinct principal curvatures and focal submanifo…
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…
Isoparametric foliations and critical sets of eigenfunctions
Zizhou Tang, Wenjiao Yan
Jakobson and Nadirashvili \cite{JN} constructed a sequence of eigenfunctions on with a bounded number of critical points, answering in the negative the question raised by Yau…
Isoparametric foliation and Yau conjecture on the first eigenvalue
ZiZhou Tang, Wenjiao Yan
A well known conjecture of Yau states that the first eigenvalue of every closed minimal hypersurface in the unit sphere is just its dimension . The present pa…
New examples of Willmore submanifolds in the unit sphere via isoparametric functions
Zizhou Tang, Wenjiao Yan
An isometric immersion is called Willmore if it is an extremal submanifold of the Willmore functional: , where…
Schoen-Yau-Gromov-Lawson theory and isoparametric foliations
Zizhou Tang, Yuquan Xie, Wenjiao Yan
Motivated by the celebrated Schoen-Yau-Gromov-Lawson surgery theory on metrics of positive scalar curvature, we construct a double manifold associated with a minimal isoparametric…
A Filtration for Isoparametric Hypersurfaces in Riemannian Manifolds
Jianquan Ge, Zizhou Tang, Wenjiao Yan
This paper introduces the notion of -isoparametric hypersurface in an -dimensional Riemannian manifold for . Many fundamental and interesting results (toward…