Kapouleas, Nikolaos; Wiygul, David The index and nullity of the Lawson surfaces \(\xi_{g,1}\). (English) Zbl 1437.53049 Camb. J. Math. 8, No. 2, 363-405 (2020). Summary: We prove that the Lawson surface \(\xi_{g,1}\) in Lawson’s original notation, which has genus \(g\) and can be viewed as a desingularization of two orthogonal great two-spheres in the round three-sphere \(\mathbb{S}^3\), has index \(2g + 3\) and nullity 6 for any genus \(g \geq 2\). In particular \(\xi_{g,1}\) has no exceptional Jacobi fields, which means that it cannot “flap its wings” at the linearized level and is \(C^1\)-isolated. Cited in 9 Documents MSC: 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) Keywords:genus, desingularization, cone construction, eigenvalue equivalence, spherical geometry, tessellations, Jacobi fields, Eigenfunctions PDFBibTeX XMLCite \textit{N. Kapouleas} and \textit{D. Wiygul}, Camb. J. Math. 8, No. 2, 363--405 (2020; Zbl 1437.53049) Full Text: arXiv