Lower bounds for index of Wente tori (Q5952190)

The authors consider the so-called original Wente tori [see \textit{R. Walter}, Geom. Dedicata 23, 187-213 (1987; Zbl 0615.53050)] which are surfaces of constant mean curvature and which have one family of planar curvature lines. They show that the Morse index of any of these constant mean curvature tori has the lower bound 8. Using results of the third author [An. Acad. Bras. Ciênc. 71, No. 4, Pt. I, 607-613 (1999; Zbl 0977.53004)] they find out that the index of almost all these tori is at least eight. Therefore, it suffices to investigate only a finite number of these constant mean curvature tori. From an explicit computation of the eigenvalues of appropriately chosen \(9\times 9\) matrices it follows that the index of these ``exceptional'' Wente tori is at least eight, too.