Closed geodesics in homology classes for convex co-compact hyperbolic manifolds

被引：2

作者：

McGowan, J

Perry, P

机构：

[1] Cent Connecticut State Univ, Dept Math, New Britain, CT 06050 USA

[2] Univ Kentucky, Dept Math, Lexington, KY 40506 USA

来源：

GEOMETRIAE DEDICATA | 2002年 / 91卷 / 01期

基金：

美国国家科学基金会;

关键词：

closed geodesics; hyperbolic manifolds; Selberg trace formula;

D O I：

10.1023/A:1016226616826

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let Gamma be a convex co-compact, torsion-free, discrete roup of isometries of real hyperbolic space Hn+1. We compute the asymptotics of the countin function for closed geodesics in homology classes for the quotient manifold X = Gamma\Hn+1, under the assumption that H-1(X, Z) is infinite. Our results imply asymptotic equipartition of geodesics in distinct homology classes.

引用

页码：197 / 209

页数：13

共 25 条

[1] Closed geodesics in homology classes on hyperbolic manifolds with cusps
Babillot, M
Peigne, M
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1997, 324 (08): : 901 - 906
[2] Bunke M, 2000, J FUNCT ANAL, V172, P76
[3] de Rham G., 1984, Differentiable Manifolds: Forms, Currents, Harmonic Forms
[4] Elstrodt J., 1998, GROUPS ACTING HYPERB, DOI 10.1007/978-3-662-03626-6
[5] EPSTEIN CL, 1985, MEM AM MATH SOC, V58, P1
[6] ASYMPTOTICS FOR CLOSED GEODESICS IN A HOMOLOGY CLASS, THE FINITE VOLUME CASE
EPSTEIN, CL
[J]. DUKE MATHEMATICAL JOURNAL, 1987, 55 (04) : 717 - 757
[7] FRIED D, 1986, ANN SCI ECOLE NORM S, V19, P491
[8] GUILLOPE L, 1994, OSAKA J MATH, V31, P247
[9] GUILLOPE L, 1992, ADV STUD PURE MATH, V21, P33
[10] Helling H., 1998, J. Lie Theory, V8, P1

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