Croissance des boules et des géodésiques fermées dans les nilvariétés
- 19 September 1983
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 3 (3) , 415-445
- https://doi.org/10.1017/s0143385700002054
Abstract
If (M, g) is a riemannian nilmanifold, the homothetic metrics εg˜ on the universal cover M converge in the sense of Gromov for small ε. In this convergence the volume of balls and the number of closed geodesies go to a limit, and precise asymptotic estimates are given for these numbers.Keywords
This publication has 12 references indexed in Scilit:
- Geometric properties of Heisenberg-type groupsAdvances in Mathematics, 1985
- Filling Riemannian manifoldsJournal of Differential Geometry, 1983
- Groups of polynomial growth and expanding mapsPublications mathématiques de l'IHÉS, 1981
- Riemannian nilmanifolds attached to Clifford modulesGeometriae Dedicata, 1981
- Principe de moindre action, propagation de la chaleur et estimees sous elliptiques sur certains groupes nilpotentsActa Mathematica, 1977
- Orbits of Families of Vector Fields and Integrability of DistributionsTransactions of the American Mathematical Society, 1973
- Orbits of families of vector fields and integrability of distributionsTransactions of the American Mathematical Society, 1973
- Growth of finitely generated solvable groups and curvature of Riemannian manifoldsJournal of Differential Geometry, 1968
- On proximity geometry of Riemannian manifoldsAmerican Mathematical Society Translations: Series 2, 1964
- Normal and Integral CurrentsAnnals of Mathematics, 1960