Inégalités isosystoliques conformes pour la bouteille de Klein. (Conformal isosystolic inequalities for the Klein bottle) (Q1117471)

It is known [the author, Math. Ann. 274, 439-441 (1986; Zbl 0578.53032)] that for every continuous Riemannian metric g on the Klein bottle one has \(area/systole^ 2\geq 2\sqrt{2}/\pi\) \((systole=\min imum\) length of non- contractible curves). Here the author improves this result to sharp inequalities \(area/systole^ 2\geq C(g)\) where C depends only on the conformal class of g.