Let M be a compact n-manifold of positive sectional curvature.We will review classical results on the fundamental group of M,a motivation on the c(n)-cyclic conjecture that the fundamental group of M contains a cyclic...Let M be a compact n-manifold of positive sectional curvature.We will review classical results on the fundamental group of M,a motivation on the c(n)-cyclic conjecture that the fundamental group of M contains a cyclic subgroup of index bounded above by c(n),a constant depending only on n,and we will survey partial results(up to date)on the c(n)-cyclic conjecture.展开更多
In this paper,we derive the sub-Riemannian version of the Kastler-Kalau-Walze type theorem and the Dabrowski-Sitarz-Zalecki type theorem for the twisted BCV spaces.We also compute the Connes conformal invariants for t...In this paper,we derive the sub-Riemannian version of the Kastler-Kalau-Walze type theorem and the Dabrowski-Sitarz-Zalecki type theorem for the twisted BCV spaces.We also compute the Connes conformal invariants for the twisted product,as well as the sub-Riemannian limits of the Connes conformal invariants for the twisted BCV spaces.展开更多
In this paper,we studyλ-biharmonic hypersurfaces M_(r)^(5) of 6-dimensional pseudo Riemannian space form N_(p)^(6)(c)with the indexs 0≤p≤6,r=p−1 or p,and constant curvature c.It was proved that if the shape operato...In this paper,we studyλ-biharmonic hypersurfaces M_(r)^(5) of 6-dimensional pseudo Riemannian space form N_(p)^(6)(c)with the indexs 0≤p≤6,r=p−1 or p,and constant curvature c.It was proved that if the shape operator of M_(r)^(5) is diagonalizable,then the mean curvature is a constant.As an application,we find some types of biharmonic hypersurfaces of N_(p)^(6)(c)are minimal.展开更多
设F1和F2分别是光滑流形M1和M2上的芬斯勒度量,共形双扭曲积芬斯勒度量是在乘积流形M=M1×M2上赋予的芬斯勒度量F2=e2σ(f22F12+f12F22), 其中f1、f2和 σ分别是M1 、M2和M上的正值光滑函数。本文证明了半C-可约共形双扭曲积芬斯勒...设F1和F2分别是光滑流形M1和M2上的芬斯勒度量,共形双扭曲积芬斯勒度量是在乘积流形M=M1×M2上赋予的芬斯勒度量F2=e2σ(f22F12+f12F22), 其中f1、f2和 σ分别是M1 、M2和M上的正值光滑函数。本文证明了半C-可约共形双扭曲积芬斯勒度量是类C2芬斯勒度量。Let F1 and F2 be two Finsler metrics on smooth manifold M1 and M2,respectively.The conformally doubly warped product Finsler metric F2=e2σ(f22F12+f12F22) is a Finsler metric endowed on the M=M1×M2 ,where f1、f2 and σ are positive smooth functions on M1 、M2 and M, respectively.It is proved that semi-C-reducible conformally doubly warped product Finsler metric is a C2-like Finsler metric.展开更多
Two sharp Chernoff type inequalities are derived for star bodies in R2,one is an extension of the dual Chernoff-Ou-Pan inequality,and the other is the reverse Chernoff type inequality.Furthermore,we establish a genera...Two sharp Chernoff type inequalities are derived for star bodies in R2,one is an extension of the dual Chernoff-Ou-Pan inequality,and the other is the reverse Chernoff type inequality.Furthermore,we establish a generalized dual symmetric mixed Chernoff inequality for two planar star bodies.As a direct consequence,a new proof of the dual symmetric mixed isoperimetric inequality is presented.展开更多
文摘Let M be a compact n-manifold of positive sectional curvature.We will review classical results on the fundamental group of M,a motivation on the c(n)-cyclic conjecture that the fundamental group of M contains a cyclic subgroup of index bounded above by c(n),a constant depending only on n,and we will survey partial results(up to date)on the c(n)-cyclic conjecture.
基金Supported by Science and Technology Development Plan Project of Jilin Province China(Grant No.20260102245JC)Supported by National Natural Science Foundation of China(Grant No.11771070).
文摘In this paper,we derive the sub-Riemannian version of the Kastler-Kalau-Walze type theorem and the Dabrowski-Sitarz-Zalecki type theorem for the twisted BCV spaces.We also compute the Connes conformal invariants for the twisted product,as well as the sub-Riemannian limits of the Connes conformal invariants for the twisted BCV spaces.
基金Supported by National Natural Science Foundation of China(12161078)Foundation for Innovative Fundamental Research Group Project of Gansu Province(24JRRA778)Project of Northwest Normal University(20240010)。
文摘In this paper,we studyλ-biharmonic hypersurfaces M_(r)^(5) of 6-dimensional pseudo Riemannian space form N_(p)^(6)(c)with the indexs 0≤p≤6,r=p−1 or p,and constant curvature c.It was proved that if the shape operator of M_(r)^(5) is diagonalizable,then the mean curvature is a constant.As an application,we find some types of biharmonic hypersurfaces of N_(p)^(6)(c)are minimal.
文摘设F1和F2分别是光滑流形M1和M2上的芬斯勒度量,共形双扭曲积芬斯勒度量是在乘积流形M=M1×M2上赋予的芬斯勒度量F2=e2σ(f22F12+f12F22), 其中f1、f2和 σ分别是M1 、M2和M上的正值光滑函数。本文证明了半C-可约共形双扭曲积芬斯勒度量是类C2芬斯勒度量。Let F1 and F2 be two Finsler metrics on smooth manifold M1 and M2,respectively.The conformally doubly warped product Finsler metric F2=e2σ(f22F12+f12F22) is a Finsler metric endowed on the M=M1×M2 ,where f1、f2 and σ are positive smooth functions on M1 、M2 and M, respectively.It is proved that semi-C-reducible conformally doubly warped product Finsler metric is a C2-like Finsler metric.
基金supported by the Postgraduate Scientic Research Innovation Project of Chongqing Normal University(YKC24010)Chunna Zeng's research was supported by the Major Special Project of the National Natural Science Foundation of China(12141101)+2 种基金the Young Top-Talent program of Chongqing(CQYC2021059145)the Technology Research Foundation of Chongqing Educational committee(KJZD-K202200509)the Natural Science Foundation Project of Chongqing(CSTB2024NSCQ-MSX0937)。
文摘Two sharp Chernoff type inequalities are derived for star bodies in R2,one is an extension of the dual Chernoff-Ou-Pan inequality,and the other is the reverse Chernoff type inequality.Furthermore,we establish a generalized dual symmetric mixed Chernoff inequality for two planar star bodies.As a direct consequence,a new proof of the dual symmetric mixed isoperimetric inequality is presented.
