Adiabatic limits, vanishing theorems and the noncommutative residue

被引:0
作者
KeFeng Liu
Yong Wang
机构
[1] Zhejiang University,Center of Mathematical Sciences
[2] University of California at Los Angeles,Department of Mathematics
[3] Northeast Normal University,School of Mathematics and Statistics
来源
Science in China Series A: Mathematics | 2009年 / 52卷
关键词
foliations; adiabatic limits; vanishing theorems; noncommutative residue; 53C27; 51H25; 46L87;
D O I
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中图分类号
学科分类号
摘要
In this paper, we compute the adiabatic limit of the scalar curvature and prove several vanishing theorems by taking adiabatic limits. As an application, we give a Kastler-Kalau-Walze type theorem for foliations.
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页码:2699 / 2713
页数:14
相关论文
共 15 条
  • [1] Liu K.(2001)On elliptic genera and foliations Math Res Lett 8 361-376
  • [2] Ma X.(1999)Adiabatic limits and spectral geometry of foliations Math Ann 313 763-783
  • [3] Zhang W.(2000)Adiabatic limits and spectral sequences for Riemannian foliations Geom Funct Anal 10 977-1027
  • [4] Kordyukov Y.(2000)Sub-Riemannian limit of the differential form spectrum of contact manifolds Geom Funct Anal 10 407-452
  • [5] López J. A.(1989)A local index theorem for non-Kähler manifolds Math Ann 284 681-699
  • [6] Kordyukov Y. A.(1984)Local invariants of spectral asymmetry Invent Math 75 143-177
  • [7] Rumin M.(2005)Spin Differential Geom Appl 22 229-252
  • [8] Bismut J. M.(1995)-structures and Dirac operators on contact manifolds Comm Math Phys 166 633-643
  • [9] Wodzicki M.(1995)The Dirac operator and gravitation J Geom Phys 16 327-344
  • [10] Petit R.(1996)Gravity, non-commutative geometry and the Wodzicki residue J Geom Phys 20 404-406