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1.
标量曲率Finsler空间与Finsler度量的射影变换 总被引:1,自引:0,他引:1
本文研究了与一个Ricci平坦Finsler空间或一个常曲率Finsler空间射影相关的标量曲率Finsler空间.我们给出了这种标量曲率Finsler空间成为常曲率空间的充分必要条件.特别地,我们给出了射影平坦Finsler空间具有常曲率的条件. 相似文献
2.
ON SYMMETRIC SCALAR CURVATURE ON 总被引:1,自引:0,他引:1
JI Min 《数学年刊B辑(英文版)》1999,20(3):325-330
1.IntroductionGivenacontinuousfunctionRonthestandardsphereS',itisaninterestingproblemwhetherRcanbethescalarcurvatureofsomemetricgwhichispointwiseconformaltothestandardmetricgoonS2.Ifwesetg~e"go,whereuisafunctiononS',theproblemisequivalenttothesolvabilityofthefollowingPDE:--A..u 2--Re"=0,onS2.(l'1)KazdanandWarner[9]pointedoutthatitmaybeinsolvable.Inthelastfewyears,alotofworkhasbeendonetosolveproblem(l.l),especiallywhenRpossessessomekindsofsymmetries.AfterthepioneerworkduetoMoser[lo]forthe… 相似文献
3.
Let f : M^n→S^n 1真包含于R^n 2 be an n-dimensional complete oriented Riemannian manifold minimally immersed in an (n 1)-dimensional unit sphere S^n 1. Denote by S^n 1 the upper closed hemisphere. If f(M^n)包含于S ^n 1, then under some curvature conditions the authors can get that the isometric immersion is a totally embedding. They also generalize a theorem of Li Hai Zhong on hypersurface of space form with costant scalar curvature. 相似文献
4.
SCALAR CURVATURES ON NONCOMPACT RIEMANN MANIFOLDS 总被引:1,自引:1,他引:0
Zhou Detang 《数学年刊B辑(英文版)》1995,16(1):87-92
SCALARCURVATURESONNONCOMPACTRIEMANNMANIFOLDS¥ZHOUDETANGAbstract:Theauthorobtainssometheoremsforafunctiontobethescalarcurvatur... 相似文献
5.
COMPLETE HYPERSURFACES WITH CONSTANT SCALAR CURVATURE IN A SPECIAL KIND OF LOCALLY SYMMETRIC MANIFOLD 下载免费PDF全文
Yingbo Han & Shuxiang Feng 《分析论及其应用》2012,28(2):189-200
In this paper, we investigate n-dimensional complete and orientable hypersufaces M n (n ≥ 3) with constant normalized scalar curvature in a locally symmetric manifold. Two rigidity theorems are obtained for these hypersurfaces. 相似文献
6.
7.
Qi S. Zhang 《Mathematische Annalen》2000,316(4):703-731
By establishing an optimal comparison result on the heat kernel of the conformal Laplacian on open manifolds with nonnegative
Ricci curvature, (a) we show that many manifolds with positive scalar curvature do not possess conformal metrics with scalar
curvature bounded below by a positive constant; (b) we identify a class of functions with the following property: If the manifold
has a scalar curvature in this class, then there exists a complete conformal metric whose scalar curvature is any given function
in this class. This class is optimal in some sense; (c) we have identified all manifolds with nonnegative Ricci curvature,
which are “uniformly” conformal to manifolds with zero scalar curvature. Even in the Euclidean case, we obtain a necessary
and sufficient condition under which the main existence results in [Ni1] and [KN] on prescribing nonnegative scalar curvature
will hold. This condition had been sought in several papers in the last two decades.
Received: 11 November 1998 / Revised: 7 April 1999 相似文献
8.
局部对称流形上的数量曲率 总被引:3,自引:0,他引:3
本文讨论了无共轭点测地线上的Jacobi声,证明了具非负数量曲率的局部对称的无共轭点流形及具非负数量曲率的具极点的局部对称的流形之数量曲率只能是零。部分解决了E.Hopf猜想。 相似文献
9.
Zhou Detang 《数学年刊B辑(英文版)》1997,18(2):173-180
CONFORMALDEFORMATIONOFCOMPLETESURFACEWITHNEGATIVECURVATUREZHOUDETANGManuscriptreceivedOctober31,1994.RevisedAugust30,1995.D... 相似文献
10.
Zhu Da xin 《数学年刊B辑(英文版)》1994,15(3):293-298
ACOMPLETEMETRICOFPOSITIVECURVATUREONR~nANDEXISTENCEOFCLOSEDGEODESICS¥ZHUDAXIN(DepartmentofMathematics,TianjinUniversitylTianj?.. 相似文献
11.
J. Kim 《Siberian Mathematical Journal》2006,47(1):64-67
We show that every compact Einstein Hermitian surface with constant conformal scalar curvature is a Kahler surface and that, in contrast to the compact case, there exits a noncompact Einstein Hermitian and non-Kahler surface with constant conformal scalar curvature. 相似文献
12.
For a supergoup , we study closed -manifolds with positive conformal classes. We use the relative Yamabe invariant from [2] to define the conformal cobordism
relation on the category of such manifolds. We prove that the corresponding conformal cobordism groups are isomorphic to the cobordism groups defined by Stolz in [19]. As a corollary, we show that the conformal concordance relation on positive conformal classes coincides
with the standard concordance relation on positive scalar curvature metrics. Our main technical tools come from analysis and
conformal geometry.
Received: 22 August 2000 / Published online: 5 September 2002 相似文献
13.
Zhang Zonglao 《Proceedings Mathematical Sciences》2005,115(3):309-318
This paper is to study the conformal scalar curvature equation on complete noncompact Riemannian manifold of nonpositive curvature.
We derive some estimates and properties of supersolutions of the scalar curvature equation, and obtain some nonexistence results
for complete solutions of scalar curvature equation. 相似文献
14.
Shen yibing 《数学年刊B辑(英文版)》1984,5(4):625-632
This paper gives some sufficient conditions for a compact submanifold with nonnegative sectional curvature in a space form to be totally umbilical. In particular, for a compact submanifold M with flat normal bundle, if the scalar curvature is proportional to the mean curvature everywhere, then M is totally umbilical or the Riemannian product of several totally umbilical constantly curved submanifolds. 相似文献
15.
聂昌雄 《数学年刊A辑(中文版)》2015,36(1):59-68
[Nie C X,Wu C X,Regular submanifolds in the conformal space Q_p~n,ChinAnn Math,2012,33B(5):695-714]中研究了共形空间Q_s~n中的正则子流形,并引入了共形空间Q_s~n中的子流形理论.本文作者将分类共形空间Q_s~n中的Blaschke拟全脐子流形,证明伪Riemann空间形式中具有常数量曲率和平行的平均曲率向量场的正则子流形是共形空间中的Blaschke拟全脐子流形;反之,共形空间中的Blaschke拟全脐子流形共形等价于伪Riemann空间形式中具有常数量曲率和平行的平均曲率向量场的正则子流形.这一结论可看作是共形空间Q_s~n中共形迷向子流形分类定理的推广. 相似文献
16.
Man Chun Leung 《偏微分方程通讯》2013,38(3-4):367-417
This note contains considerations on the existence and non-existence problem of conformal scalar curvature equations on some complete manifolds. We impose two general types of conditions on complete manifolds. The first type is in terms of bounds on curvature and injectivity radius. The second type is in terms of some particular structures on ends of manifolds, for examples, manifolds with cones or cusps and conformally compact manifolds. We obtain non-existence results on both types of conditions. Then we study in more details the existence problem on manifolds with cones, manifolds with cusps and conformally flat manifolds of bounded positive scalar curvature. 相似文献
17.
本文研究具强负曲率Cartan-Hadamard流形M~n(n≥3)上给定数量曲率函数S的共形形变问题.利用上下解方法,并通过精心构造上解,我们获得了当完备的共形形变度量存在时,函数S在无穷远附近的最佳渐近性态.在较一般情况下,我们还给出了共形数量曲率方程解的渐近估计. 相似文献
18.
Giovanni Catino 《Advances in Mathematics》2010,223(2):393-404
In this paper we prove that, under an explicit integral pinching assumption between the L2-norm of the Ricci curvature and the L2-norm of the scalar curvature, a closed 3-manifold with positive scalar curvature admits a conformal metric of positive Ricci curvature. In particular, using a result of Hamilton, this implies that the manifold is diffeomorphic to a quotient of S3. The proof of the main result of the paper is based on ideas developed in an article by M. Gursky and J. Viaclovsky. 相似文献
19.
Using the Lyapunov–Schmidt reduction method, we describe how to use annular domains to construct (scalar curvature) functions on S n (n ≥ 6), so that each one of them enables the conformal scalar curvature equation to have a blowing-up sequence of positive solutions. The prescribed scalar curvature function is shown to have C n - 1, β smoothness. 相似文献
20.
In this article, after giving a necessary and sufficient condition for two Einstein- Weyl manifolds to be in conformal correspondence, we prove that any conformal mapping between such manifolds is generalized concircular if and only if the covector field of the conformal mapping is locally a gradient. Using this fact we deduce that any conformal mapping between two isotropic Weyl manifolds is a generalized concircular mapping. Moreover, it is shown that a generalized concircularly flat Weyl manifold is generalized concircular to an Einstein manifold and that its scalar curvature is prolonged covariant constant. 相似文献