Optimal systolic inequalities on Finsler Mobius bands

TL;DR

This paper establishes optimal systolic inequalities for Finsler Mobius bands and Klein bottles, relating geometric invariants and presenting extremal metrics, advancing understanding of Finsler geometry in non-orientable surfaces.

Contribution

It proves new optimal inequalities for Finsler Mobius bands and Klein bottles, including extremal metric families, and conjectures broader applicability for Klein bottles.

Findings

Optimal systolic inequalities for Finsler Mobius bands.

Optimal systolic inequality for Finsler Klein bottles of revolution.

Presentation of extremal metric families.

Abstract

We prove optimal systolic inequalities on Finsler Mobius bands relating the systole and the height of the Mobius band to its Holmes-Thompson volume. We also establish an optimal systolic in- equality for Finsler Klein bottles of revolution, which we conjecture to hold true for arbitrary Finsler metrics. Extremal metric families both on the Mobius band and the Klein bottle are also presented.