Hyperellipticity and Klein bottle companionship in systolic geometry

2008/11/11 by Karin U. Katz, Karin Usadi Katz, Katz, Karin Usadi +2
Mathematics · #30F10 #53C23 #58J60 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #math.AG #math.DG #msc:30F10 #msc:53C23 #msc:58J60

paper · pdf · doi:10.48550/arxiv.0811.1717

18 pages, 1 figure

openalex publication_date 2008/11/11 · arxiv created 2009/05/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a hyperelliptic Klein surface, we construct companion Klein bottles. Bavard's short loops on companion bottles are studied in relation to the surface to improve an inequality of Gromov's in systolic geometry.

Citations

• Systolic inequalities and minimal hypersurfaces

Cited by

• Cohomological dimension, self-linking, and systolic geometry
• Hurwitz quaternion order and arithmetic Riemann surfaces

Related

• Stability of systolic inequalities for the Möbius strip and Klein bottle
• Conformal Geometric Inequalities on the Klein Bottle
• Geodesic length spectrum of hyperelliptic connected components
• Systolic freedom of orientable manifolds
• Translation surfaces with large systoles