共查询到20条相似文献,搜索用时 31 毫秒
1.
Wilderich TUSCHMANN 《Frontiers of Mathematics in China》2016,11(5):1335-1343
These notes present and survey results about spaces and moduli spaces of complete Riemannian metrics with curvature bounds on open and closed manifolds, here focussing mainly on connectedness and disconnectedness properties. They also discuss several open problems and questions in the field. 相似文献
2.
Yi SHI . Guanghan LI . Chuarixi WU 《数学年刊B辑(英文版)》2014,35(1):93-100
In this paper, the relationship between the existence of closed geodesics and the volume growth of complete noncompact Riemannian manifolds is studied. First the authors prove a diffeomorphic result of such an n-m2nifold with nonnegative sectional curvature, which improves Marenich-Toponogov's theorem. As an application, a rigidity theorem is obtained for nonnegatively curved open manifold which contains a clesed geodesic. Next the authors prove a theorem about the nonexistence of closed geodesics for Riemannian manifolds with sectional curvature bounded from below by a negative constant. 相似文献
3.
《Expositiones Mathematicae》2021,39(4):566-582
We discuss the geography problem of closed oriented 4-manifolds that admit a Riemannian metric of positive scalar curvature, and use it to survey mathematical work employed to address Gromov’s observation that manifolds with positive scalar curvature tend to be inessential by focusing on the four-dimensional case. We also point out an strengthening of a result of Carr and its extension to the non-orientable realm. 相似文献
4.
A classical result in differential geometry assures that the total torsion of a closed spherical curve in the three-dimensional
space vanishes. Besides, if a surface is such that the total torsion vanishes for all closed curves, it is part of a sphere
or a plane. Here we extend these results to closed curves in three dimensional Riemannian manifolds with constant curvature.
We also extend an interesting companion for the total torsion theorem, which was proved for surfaces in by L. A. Santaló, and some results involving the total torsion of lines of curvature.
Dedicated to Professor Manfredo P. do Carmo on his 80th birthday. 相似文献
5.
Mingliang Cai 《Annals of Global Analysis and Geometry》1993,11(4):373-385
Cheeger and Gromoll proved that a closed Riemannian manifold of nonnegative Ricci curvature is, up to a finite cover, diffeomorphic to a direct product of a simply connected manifold and a torus. In this paper, we extend this theorem to manifolds of almost nonnegative Ricci curvature. 相似文献
6.
We prove that a Finsler manifold with vanishing Berwald scalar curvature has zero E-curvature. As a consequence, Landsberg manifolds with vanishing Berwald scalar curvature are Berwald manifolds. For (α,β)-metrics on manifold of dimension greater than 2, if the mean Landsberg curvature and the Berwald scalar curvature both vanish, then the Berwald curvature also vanishes. 相似文献
7.
§1. IntroductionLetMbeann-dimensionalconformallyflatmanifoldwithconstantscalarcurvatureρ(n≥3).WhentheRiccicurvatureSofMisofboundedbelowandySy2<ρ2/(n-1),Gold-bergprovedthatMisofconstantcurvature[1].WhenMisacompactmanifoldwithpositiveRiccicurvature,WuB… 相似文献
8.
Y. F. Chen 《数学年刊B辑(英文版)》2016,37(3):451-464
The author studies the properties and applications of quasi-Killing
spinors and quasi-twistor spinors and obtains some vanishing
theorems. In particular, the author classifies all the types of
quasi-twistor spinors on closed Riemannian spin manifolds. As a
consequence, it is known that on a locally decomposable closed spin
manifold with nonzero Ricci curvature, the space of twistor spinors
is trivial. Some integrability condition for twistor spinors is also
obtained. 相似文献
9.
Bing-ye WU Department of Mathematics Minjiang University Fuzhou China 《中国科学A辑(英文版)》2007,50(5):609-614
In this paper we study a global rigidity property for weakly Landsberg manifolds and prove that a closed weakly Landsberg manifold with the negative flag curvature must be Riemannian. 相似文献
10.
李奇曲率平行的黎曼流形的曲率张量模长 总被引:2,自引:2,他引:0
李安民和赵国松[1]提出了下面的问题:找出李奇曲率平行的黎曼流形的曲率张量模长的最佳拼挤常数并确定达到该值的流形.本文确定了非爱因斯坦流形的最佳拼挤常数和达到该值的黎曼流形.在n12时,回答了[1]中提出的问题. 相似文献
11.
邓义华 《数学的实践与认识》2010,40(23)
讨论了具有相对迷向平均Landsberg曲率的度量的一些几何性质.证明了任一闭的具有负旗曲率与相对迷向平均Landsberg曲率的流形一定是Riemann流形. 相似文献
12.
We study manifolds where the natural skew-symmetric curvature operator has pointwise constant eigenvalues. We give a local classification (up to isometry) of such manifolds in dimension 4. In dimension 3, we describe such manifolds up to a classification of three - dimensional Riemannian manifolds with principal Ricci curvatures r1 = r2 = 0, r3- arbitrary. We give examples of such manifolds in all dimensions which do not have constant sectional curvature; these manifolds are not pointwise Osserman manifolds in general. 相似文献
13.
We prove the existence of infinite-dimensional families of(non-Kähler) almost-Kähler metrics with constant scalar curvature oncertain compact manifolds. These are obtained by deformingconstant-scalar-curvature Kähler metrics on suitable compact complexmanifolds. We prove several other similar results concerning the scalarcurvature and/or the *-scalar curvature. We also discuss thescalar curvature functions of almost-Kähler metrics. 相似文献
14.
For a closed curve in a CAT(K) space with given circumradius and upper bound on curvature, a basic lower bound on the length is established. The inequality is sharp, assumed only when the curve is the boundary of an isometric copy of a racetrack (the convex hull of two congruent circles) from a plane of constant curvature K. Previously such a theorem was proved for Euclidean plane curves by G.D.Chakerian, H.H. Johnson, and A. Vogt, and for curves in higher dimensional Euclidean spaces by A.D. Milka. A similar theorem is proved for nonclosed curves, with a notion of breadth replacing circumradius. Thus we illustrate how singular methods can extend classical Euclidean theorems to a large class of new spaces (including Riemannian manifolds of curvature bounded above) and also give significant strengthenings even in Euclidean space. 相似文献
15.
ZHOU Detang 《数学年刊B辑(英文版)》2003,24(3):285-292
The author obtains the theorems of Barth-Lefschetz type on Kahler manifolds with partially positive bisectional curvature without the assumption of nonnegative bisectional curvature. Some applications of the results to holomorphic mappings are given. 相似文献
16.
We present a classification of complete locally irreducible Riemannian manifolds with nonnegative curvature operator, which admit a nonzero and nondecomposable harmonic form with its square-integrable norm. We prove a vanishing theorem for harmonic forms on complete generic Riemannian manifolds with nonnegative curvature operator. We obtain similar results for closed and co-closed conformal Killing forms. 相似文献
17.
Finsler空间上的Weyl曲率 总被引:1,自引:0,他引:1
MoXiaohuan 《高校应用数学学报(英文版)》2005,20(1):10-20
The Weyl curvature of a Finsler metric is investigated. This curvature constructed from Riemannain curvature. It is an important projective invariant of Finsler metrics. The author gives the necessary conditions on Weyl curvature for a Finsler metric to be Randers metric and presents examples of Randers metrics with non-scalar curvature. A global rigidity theorem for compact Finsler manifolds satisfying such conditions is proved. It is showed that for such a Finsler manifold,if Ricci scalar is negative,then Finsler metric is of Randers type. 相似文献
18.
19.
Lin Feng Wang 《Journal of Differential Equations》2018,264(1):506-524
In this paper, by a regularization process we derive new gradient estimates for positive solutions to the weighted p-Laplace heat equation when the m-Bakry–Émery curvature is bounded from below by ?K for some constant . When the potential function is constant, which reduce to the gradient estimate established by Ni and Kotschwar for positive solutions to the p-Laplace heat equation on closed manifolds with nonnegative Ricci curvature if , and reduce to the Davies, Hamilton and Li–Xu's gradient estimates for positive solutions to the heat equation on closed manifolds with Ricci curvature bounded from below if . 相似文献
20.
Tiago Caúla Levi Lopes de Lima Newton Luis Santos 《Mathematische Nachrichten》2013,286(17-18):1752-1777
We present several deformation and rigidity results within the classes of closed Riemannian manifolds which either are 2k‐Einstein (in the sense that their 2k‐Ricci tensor is constant) or have constant 2k‐Gauss‐Bonnet curvature. The results hold for a family of manifolds containing all non‐flat space forms and the main ingredients in the proofs are explicit formulae for the linearizations of the above invariants obtained by means of the formalism of double forms. 相似文献