Survey on optimal isosystolic inequalities on the real projective plane

Authors

Keywords:

real projective plane, systole, isosystolic inequality, Riemannian metric, Finsler metric, Busemann–Hausdorff area, Holmes–Thompson area.

Abstract

All known optimal isosystolic inequalities on the real projective plane RP2 are surveyed, comparing them to the case of the 2-torus T2. First, basic notions on Finsler metrics are introduced. Then, all previously known isosystolic inequalities are stated and a sketch of proof is given in the reversible case. Finally, optimal inequalities in the non-reversible case are discussed. All optimal inequalities are currently known for T2, although this is not the case for RP2. Some recent minor advances for RP2 are presented, and some arguments are given in favour of the conjectured inequality in the remaining open case.

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How to Cite

Lejarza Alonso, U. (2024). Survey on optimal isosystolic inequalities on the real projective plane. Reports@SCM, 9(1), 21–30. Retrieved from https://revistes.iec.cat/index.php/reports/article/view/154338

Issue

Vol. 9 No. 1 (2024)

Section

Articles

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