The Ricci Flow on Noncommutative Two-Tori

被引：0
作者：
Tanvir Ahamed Bhuyain
Matilde Marcolli
机构：
[1] California Institute of Technology,Department of Mathematics
来源：
Letters in Mathematical Physics | 2012年 / 101卷
关键词：
58J42; 58B34; Ricci flow; noncommutative tori; pseudodifferential calculus;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper we construct a version of Ricci flow for noncommutative two-tori, based on a spectral formulation in terms of the eigenvalues and eigenfunction of the Laplacian and recent results on the Gauss–Bonnet theorem for noncommutative tori.
引用
收藏
页码：173 / 194
页数：21
相关论文
共 56 条
  • [1] Anderson M.T.(2004)Geometrization of 3-manifolds via the Ricci flow Notices Am. Math. Soc. 51 184-193
  • [2] Bañados M.(1992)Black hole in three-dimensional spacetime Phys. Rev. Lett. 69 1849-1851
  • [3] Teitelboim C.(1983)Generic properties of the eigenvalue of the Laplacian for compact Riemannian manifolds Tohoku Math. J. (2) 35 155-172
  • [4] Zanelli J.(1973)Sur les premières valeurs propres des varités riemanniennes Compositio Math. 26 129-149
  • [5] Bando S.(1999)Geometrical finiteness, holography, and the Bañados–Teitelboim–Zanelli black hole Phys. Rev. Lett. 82 4164-4167
  • [6] Urakawa H.(2007)Eigenvalues of − Δ + R/2 on manifolds with nonnegative curvature operator Math. Ann. 337 435-441
  • [7] Berger M.(2008)First eigenvalues of geometric operators under the Ricci flow Proc. Am. Math. Soc. 136 4075-4078
  • [8] Birmingham D.(1997)The spectral action principle Commun. Math. Phys. 186 731-750
  • [9] Kennedy C.(1991)The Ricci flow on the 2-sphere J. Differ. Geom. 33 325-334
  • [10] Sen S.(1980) algèbres et géométrie différentielle C. R. Acad. Sci. Paris Sér. A-B 290 A599-A604
123456