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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Prescribing sigma-2 curvature and boundary mean curvature on compact manifolds
紧致流形 sigma-2曲率 边界平均曲率
2023/11/15
On a smooth compact manifold of dimensions three and four with totally non-umbilic boundary，imposing non-negativity assumptions on curvatures of the background metric, we establish that there exists a...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Liouville Properties on gradient shrinking Ricci solitons with constant scalar curvature
常标量 曲率梯度收缩 Ricci孤子 Liouville性质
2023/11/13
In this talk we show that bounded harmonic functions are constant on gradient shrinking Ricci solitons with CSC by frequency function method. As an application, we show that the space of harmonic func...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Researches on manifolds with scalar curvature bounded from below
标量曲率 有界 流形
2023/4/25
The motivation to study manifolds with scalar curvature bounded from below comes from Mathematical General Relativity and Riemannian Geometry. In this talk, I'll first briefly introduce some problems ...
A large class of non constant mean curvature solutions of the Einstein constraint equations on an asymptotically hyperbolic manifold
Asymptotically hyperbolic manifold Constraint equations Conformal method
2011/3/2
We construct solutions of the constraint equation with non constant mean curvature on an
asymptotically hyperbolic manifold by the conformal method. Our approach consists in decreasing a certain expo...
It is proved that the fundamental group of the space of harmonic polynomials of degree n(n ≥ 2), with the same Gaussian curvature is not trivial. Furthermore, we give an example of topologically noneq...
We introduce a parabolic flow of almost K¨ahler structures, providing a natural extension of K¨ahler Ricci flow onto symplectic manifolds. We exhibit this flow as one of a family of parabolic flows of...
AH3-manifolds of constant antiholomorphic sectional curvature
AH3-manifolds constant antiholomorphic sectional curvature
2010/12/6
The purpose of this paper is to prove that an AH3-manifold of constant antiholomorphic sectional curvature is a real space form or a complex space form.
Almost Kähler manifolds of constant antiholomorphic sectional curvature
Kä hler manifolds constant antiholomorphic sectional curvature
2010/12/6
We prove that an AK2-manifold of dimension 2m ≥ 6 and of pointwise constant antiholomorphic
sectional curvature is either a 6-dimensional manifold of constant negative sectional curvature or is local...
Nearly Kähler manifolds of constant antiholomorphic sectional curvature
Kä hler manifolds constant antiholomorphic sectional curvature
2010/12/6
In this paper we consider nearly K¨ahler manifolds of pointwise constant antiholomorphic
sectional curvature. An analogue of Schur’s theorem is proved and a classification theorem
for such manifolds...
Curvature estimates for submanifolds in warped products
Warped product manifolds Omori-Yau maximum principle weak Omori-Yau maximum principle
2010/12/8
We give estimates on the intrinsic and the extrinsic cur-vature of manifolds that are isometrically immersed as cylindrically bounded submanifolds of warped products. We also address extensions of the...
On Some Finsler Metrics of Constant (or scalar) Flag Curvature
Finsler metric flag curvature Zermelo navi- gation problem constant curvature
2015/5/6
This paper gives a lot of new Finsler metrics of scalar curvature. In partic-ular, we show at least there is an n(n−1)2-dimensional family of new Finsler metrics of constant flag curvature.