Sectional Curvature Rigidity of Asymptotically Locally Hyperbolic Manifolds

被引：0
作者：
Mario Listing
机构：
[1] Stony Brook University,Department of Mathematics
来源：
Annals of Global Analysis and Geometry | 2004年 / 25卷
关键词：
hyperbolic quotient; rigidity; special Killing form;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper presents a rigidity result of real hyperbolic quotients inanalogy to Min-Oo's result in Math. Ann.285(4) (1989),527–539, but without the spin condition. In order to prove this,we use special Killing forms on the exterior form bundle. Moreover, wemake an assumption on the sectional curvature to obtain the necessaryeigenvalue estimates of the curvature endomorphism in theBochner–Weitzenböck formula of ΩkM.
引用
收藏
页码：353 / 364
页数：11
相关论文
共 19 条
[1]  
Andersson L.(1998)Scalar curvature rigidity for asymptotically locally hyperbolic manifolds Ann. Global Anal. Geom. 16 1-27
[2]  
Dahl M.(1998)Comparison and rigidity theorems in semi-Riemannian geometry Comm. Anal. Geom. 6 819-877
[3]  
Andersson L.(1986)The mass of an asymptotically flat manifold Comm. Pure Appl. Math. 39 661-693
[4]  
Howard R.(1975)Opérateur de courbure et laplacien des formes différentielles d'une variété riemannienne J. Math. Pures Appl. (9) 54 259-284
[5]  
Bartnik R.(1991)Einstein metrics with prescribed conformal infinity on the ball Adv. Math. 87 186-225
[6]  
Gallot S.(1982)Gap theorems for noncompact Riemannian manifolds Duke Math. J. 49 731-756
[7]  
Meyer D.(1983)Positive scalar curvature and the Dirac operator on complete Riemannian manifolds Inst. Hautes Études Sci. Publ. Math. 58 83-196
[8]  
Graham C. R.(1988)Counter-examples to the generalized positive action conjecture Comm. Math. Phys. 118 591-596
[9]  
Lee J. M.(1987)The Yamabe problem Bull. Amer. Math. Soc. (N.S.0029 17 37-91
[10]  
Greene R. E.(1989)Scalar curvature rigidity of asymptotically hyperbolic spin manifolds Math. Ann. 285 527-539
12