VOLUMES OF GEODESIC BALLS IN HEISENBERG GROUPS H5

Let H5 be the 5-dimensional Heisenberg group equipped with a left-invariant metric. In this paper we calculate the volumes of geodesic balls in H5ㆍLet Be (R) be the geodesic ball with center e (the identity of H5 ) and radius R in H5. Then, the volume of Be(R) is given by where p n and q n are polynomials with degree n.

1. Introduction

2. Preliminaries

3. Proof of main theorem

(0)

(0)

(0)

(0)