Lengths of geodesics on non-orientable hyperbolic surfaces

2006/12/05 by Norbury, Paul · 3 citations
#30F60 #32G15 #58D27 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.math/0612128

Abstract

We give an identity involving sums of functions of lengths of simple closed geodesics, known as a McShane identity, on any non-orientable hyperbolic surface with boundary which generalises Mirzakhani's identities on orientable hyperbolic surfaces with boundary.

Cited by

• Volumes of moduli spaces of bordered Klein surfaces
• Uniqueness of Maximal Curve Systems on Punctured Projective Planes
• Topological gravity for arbitrary Dyson index

Related

• Geodesic and orthogeodesic identities on hyperbolic surfaces
• A McShane-type identity for closed surfaces
• Minimal length of nonsimple closed geodesics on hyperbolic surfaces
• McShane's identity for classical Schottky Groups
• McShane-type Identities for Affine Deformations