三维洛伦兹李群上关于Bott联络的左不变Ricci共线

研究了三维洛伦兹李群关于不同分裂下的Bott联络问题,在三维洛伦兹李群上,确定了关于3种不同分裂下的Bott联络的所有左不变Ricci共线.

Navigation Finsler metrics on a gradient Ricci soliton

In this paper,we study a class of Finsler metrics defined by a vector field on a gradient Ricci soliton.We obtain a necessary and sufficient condition for these Finsler metrics on a compact gradient Ricci soliton to be of isotropic S-curvature by establishing a new integral inequality.Then we determine the Ricci curvature of navigation Finsler metrics of isotropic S-curvature on a gradient Ricci soliton generalizing result only known in the case when such soliton is of Einstein type.As its application,we obtain the Ricci curvature of all navigation Finsler metrics of isotropic S-curvature on Gaussian shrinking soliton.

COMPLETE KAHLER METRICS WITH POSITIVE HOLOMORPHIC SECTIONAL CURVATURES ON CERTAIN LINE BUNDLES(RELATED TO A COHOMOGENEITY ONE POINT OF VIEW ON A YAU CONJECTURE)

In this article,we study Kahler metrics on a certain line bundle over some compact Kahler manifolds to find complete Kahler metrics with positive holomorphic sectional(or bisectional)curvatures.Thus,we apply a strategy to a famous Yau conjecture with a co-homogeneity one geometry.

Bismut Ricci 平坦双扭曲积埃尔米特流形

设(M1,g)和(M2,h)是两个埃尔米特流形, 双扭曲积埃尔米特流形 (f2M1 × f1M2,G) 是赋予了扭曲积埃尔米特度量G= f22g + f12h的乘积流形M1 × M2,其中f1和f2分别是M1和M2上的正值光滑函数。 本文给出双扭曲积埃尔米特流形的Bismut联络、Bismut曲率、Bismut Ricci曲率和Bismut标量曲率的表达式,并得到双扭曲积埃尔米特流形 Bismut Ricci 平坦的充要条件,从而给出构造 Bismut Ricci 平坦埃尔米特流形的有效方法。

梯度Ricci-Yamabe孤立子的一些刚性结果

应用散度定理及一些Riemann流形上的重要不等式,并结合几何分析的方法研究紧致梯度Ricci-Yamabe孤立子的刚性问题,在适当的条件下得到非平凡紧致梯度Ricci-Yamabe孤立子与欧氏球面等距的刚性结果.此外,在数量曲率为正的假设下,证明满足L^(n/2)-积分拼挤条件的n(4≤n≤6)维紧致梯度收缩Ricci-Yamabe孤立子一定是Einstein流形.

Distribution and correlation of refractive parameters in children with different corneal curvatures in southeast China

AIM:To analyze the distribution of refractive status in school-age children with different corneal curvatures(CC)and the correlation between CC and refractive status.METHODS:A total of 2214 school-aged children of grade 4 in Hangzhou who were screened for school myopia were included.Uncorrected distance visual acuity(UCDVA),non-cycloplegic refraction,axial length(AL),horizontal and vertical corneal curvature(K1,K2)were measured and spherical equivalent(SE),corneal curvature radius(CCR)and axial length/corneal radius of curvature ratio(AL/CR)were calculated.UCDVA<5.0 and SE≤-0.50 D were classified as school-screening myopia.According to the different CCRs,the patients were divided into the lower corneal curvature(LCC)group(CCR≥7.92)and the higher corneal curvature(HCC)group(CCR<7.92).Each group was further divided into the normal AL subgroup and the long AL subgroup.The refractive parameters were compared to identify any differences between the two groups.RESULTS:Both SE and AL were greater in the LCC group(P=0.013,P<0.001).The prevalence of myopia was 38% in the LCC group and 44% in the HCC group(P<0.001).The proportion of children without screening myopia was higher in the LCC group(62%)than in the HCC group(56%).Among these children without screening myopia,the proportion of long AL in the LCC group(24%)was significantly higher than that in the HCC group(0.012%;P<0.001).The change of SE in the LCC group was less affected by the increase of AL than that in the HCC group.CONCLUSION:School-aged children in the LCC group have a lower incidence of screening myopia and longer AL.Low CC can mask SE reduction and AL growth to some extent,and the change of AL growth change more in children with low CC than high CC.Before the onset of myopia,its growth rate is even faster than that after the onset of myopia.

THE LOGARITHMIC SOBOLEV INEQUALITY FOR A SUBMANIFOLD IN MANIFOLDS WITH ASYMPTOTICALLY NONNEGATIVE SECTIONAL CURVATURE

In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality,this inequality contains a term involving the mean curvature.

具有常数正Ricci曲率的图

本文在Lin-Lu-Yau给出的图的Ricci曲率的定义下,刻画了一类具有常数正Ricci曲率的图。更进一步地,本文找到了图上每条边的Ricci曲率都不小于1的充分必要条件,并刻画了图上每条边的Ricci曲率都等于1的图。

一类三维非单模洛伦兹李群上的代数Ricci孤立子

Ricci孤立子是一类特殊的黎曼度量,类似于Ricci曲率定号流形,是近些年研究的热点。关于具有积结构的三维洛伦兹李群与两种联络有关的代数Ricci孤立子存在情况,有学者已经给出了明确的结论。本文在现有成果的基础上,将其拓展到具体一类三维非单模左不变洛伦兹李群上与三种联络相关的两类代数Ricci孤立子存在的情形,给出了该群分别与三种联络有关的两类代数Ricci孤立子存在条件的具体结果,这对揭示李群上几何性质和拓扑性质有重要的理论研究意义。

ON A NEW DEFINITION OF RICCI CURVATURE ON ALEXANDROV SPACES

Recently, in [49], a new definition for lower Ricci curvature bounds on Alexandrov spaces was introduced by the authors. In this article, we extend our research to summarize the geometric and analytic results under this Ricci condition. In particular, two new results, the rigidity result of Bishop-Gromov volume comparison and Lipschitz continuity of heat kernel, are obtained.

Open Manifolds with Nonnegative Ricci Curvature and Large Volume Growth

In this paper, we prove that if M is an open manifold with nonnegativeRicci curvature and large volume growth, positive critical radius, then sup Cp = ∞.As an application, we give a theorem which supports strongly Petersen's conjecture.

ON SHRINKING GRADIENT RICCI SOLITONS WITH POSITIVE RICCI CURVATURE AND SMALL WEYL TENSOR

We show that closed shrinking gradient Ricci solitons with positive Ricci curvature and sufficiently pinched Weyl tensor are Einstein. When Weyl tensor vanishes, this has been proved before but our proof here is much simpler.

A DIFFERENTIABLE SPHERE THEOREM WITH PINCHING INTEGRAL RICCI CURVATURE

In this article, we introduce the Hausdorff convergence to derive a differentiable sphere theorem which shows an interesting rigidity phenomenon on some kind of manifolds.

Small Excess and the Topology of Open Manifolds with Ricci Curvature Negatively Lower Bounded

In this paper, we study the relation between the excess of open manifolds and their topology by using the methods of comparison geometry. We prove that a complete open Riemmannian manifold with Ricci curvature negatively lower bounded is of finite topological type provided that the conjugate radius is bounded from below by a positive constant and its Excess is bounded by some function of its conjugate radius, which improves some results in [4].

Ricci Curvature of Certain Submanifolds in Kenmotsu Space Forms

In this paper, we obtain some sharp inequalities between the Ricci cur- vature and the squared mean curvature for bi-slant and semi-slant submanifolds in Kenmotsu space forms. Estimates of the scalar curvature and the k-Ricci curvature, in terms of the squared mean curvature, are also proved respectively.

Complete Open Manifolds with Nonnegative Ricci Curvature

In this paper, we study complete open manifolds with nonnegative Ricci curvature and injectivity radius bounded from below. We find that this kind of manifolds are diffeomorphic to a Euclidean space when certain distance functions satisfy a reasonable condition.

弦σ模型中的Ricci流扰动和Weyl反常系数

研究d=2维时空中玻色弦σ模型,采用2种Ricci流扰动方程推导Weyl反常系数.第1种方程是引力子场Gμν\,Dilaton场Φ的双圈流方程;第2种方程是引力子场G_(μν),轴子场B_(μν)和Dilaton场Φ的单圈流方程,通过这些Ricci流方程导出引力场的扰动方程.另外,还导出Weyl反常系数β_(μν)^(G),β_(μν)^(B),β^(Φ)的表达式,分析和讨论这些β函数随动量标度λ变化的物理意义.

The Manifolds with Ricci Curvature Decay to Zero

The paper quotes the concept of Ricci curvature decay to zero. Base on this new concept, by modifying the proof of the canonical Cheeger-Gromoll Splitting Theorem, the paper proves that for a complete non-compact Riemannian manifold M with Ricci curvature decay to zero, if there is a line in M, then the isometrically splitting M = R × N is true.

Manifolds with Bakry-Emery Ricci Curvature Bounded Below

In this paper we show that, under some conditions, if M is a manifold with Bakry-émery Ricci curvature bounded below and with bounded potential function then M is compact. We also establish a volume comparison theorem for manifolds with nonnegative Bakry-émery Ricci curvature which allows us to prove a topolological rigidity theorem for such manifolds.

MANIFOLDS WITH POINTWISE PINCHED RICCI CURVATURE

In this article, the author proves a compactness result about Riemannian manifolds with an arbitrary pointwisely pinched Ricci curvature tensor.