Hyperellipticity and Klein bottle companionship in systolic geometry

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.

arXiv comment18 pages, 1 figure

References in corpus (2)

• Systolic inequalities and minimal hypersurfaces
• Cayley 4-form, comass, and triality isomorphisms

Cited by in corpus (4)

• Loewner's torus inequality with isosystolic defect
• Relative systoles of relative-essential 2-complexes
• Cohomological dimension, self-linking, and systolic geometry
• Hurwitz quaternion order and arithmetic Riemann surfaces