Nonvanishing of geodesic periods over compact hyperbolic manifolds

TL;DR

This paper proves that on compact hyperbolic manifolds of dimension three or higher, there are infinitely many nonvanishing geodesic periods over any given geodesic cycle, revealing deep geometric properties.

Contribution

It establishes the existence of infinitely many nonvanishing geodesic periods over any geodesic cycle in compact hyperbolic manifolds of dimension at least two.

Findings

Infinitely many nonvanishing geodesic periods exist

Results hold for any geodesic cycle

Applicable to manifolds of dimension three and higher

Abstract

Let $X$ be a compact hyperbolic manifold with dimension $d\geqslant3$. In this paper we show that there are infinitely many nonvanishing geodesic periods defined over any compact $n$-dimensional ($n\geqslant2$) geodesic cycle of $X$.