Killing forms on G2- and Spin7-manifolds

被引：14
|
作者：
Semmelmann, Uwe [1 ]
机构：
[1] Univ Hamburg, Fachbereich Math, D-20146 Hamburg, Germany
来源：
JOURNAL OF GEOMETRY AND PHYSICS | 2006年 / 56卷 / 09期
关键词：
special holonomy manifolds; killing forms;
D O I：
10.1016/j.geomphys.2005.10.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Killing forms on Riemannian manifolds are differential forms whose covariant derivative is totally skew-symmetric. We prove that on a compact manifold with holonomy G(2) or Spin(7) any Killing form has to be parallel. The main tool is a universal Weitzenbock formula. We show, how such a formula can be obtained for any given holonomy group and any representation defining a vector bundle. (c) 2005 Published by Elsevier B.V.
引用
收藏
页码：1752 / 1766
页数：15
相关论文
共 50 条
  • [41] SUBGROUPS OF SPIN(7) OR SO(7) WITH EACH ELEMENT CONJUGATE TO SOME ELEMENT OF G2 AND APPLICATIONS TO AUTOMORPHIC FORMS
    Chenevier, Gaetan
    DOCUMENTA MATHEMATICA, 2019, 24 : 95 - 161
  • [42] Asymptotically cylindrical 7-manifolds of holonomy G2 with applications to compact irreducible G2-manifolds
    Alexei Kovalev
    Johannes Nordström
    Annals of Global Analysis and Geometry, 2010, 38 : 221 - 257
  • [43] Intersection forms of non-spin four manifolds
    Ronnie Lee
    Tian-Jun Li
    Mathematische Annalen, 2001, 319 : 311 - 318
  • [44] On the intersection forms of spin four-manifolds with boundary
    Manolescu, Ciprian
    MATHEMATISCHE ANNALEN, 2014, 359 (3-4) : 695 - 728
  • [45] On the intersection forms of spin four-manifolds with boundary
    Ciprian Manolescu
    Mathematische Annalen, 2014, 359 : 695 - 728
  • [46] Intersection forms of non-spin four manifolds
    Lee, R
    Li, TJ
    MATHEMATISCHE ANNALEN, 2001, 319 (02) : 311 - 318
  • [47] Imaginary Killing Spinors on (2, n - 2)-Manifolds
    Shafiee, M.
    Bahrampour, Y.
    LOBACHEVSKII JOURNAL OF MATHEMATICS, 2009, 30 (01) : 81 - 88
  • [48] New complete noncompact Spin(7) manifolds
    Cvetic, M
    Gibbons, GW
    Lü, H
    Pope, CN
    NUCLEAR PHYSICS B, 2002, 620 (1-2) : 29 - 54
  • [49] On the Elliptic Genera of Manifolds of Spin(7) Holonomy
    Benjamin, Nathan
    Harrison, Sarah M.
    Kachru, Shamit
    Paquette, Natalie M.
    Whalen, Daniel
    ANNALES HENRI POINCARE, 2016, 17 (10): : 2663 - 2697
  • [50] M-theory on spin(7) manifolds
    Gukov, S
    Sparks, J
    NUCLEAR PHYSICS B, 2002, 625 (1-2) : 3 - 69
12345