Minimal Legendrian submanifolds of \(S^{2n+1}\) and absolutely area-minimizing cones
This paper gives a new and unified construction of compact homogeneous minimal Legendrian submanifolds of odd-dimensional spheres. It is shown that the cones over these submanifolds are absolutely area-minimizing. The construction is based on work of \textit{R. Harvey} and \textit{H. B. Lawson} in [Acta Math. 148, 47--157 (1982; Zbl 0584.53021)]. One family of these examples is constructed from isoparametric hypersurfaces in spheres. Another family uses orbits of isotropy representations of Hermitian symmetric spaces. Furthermore, it is shown that any Legendrian immersion of the 2-torus into the 5-sphere is regularly homotopic through Legendrian immersions to a minimal Legendrian embedding if and only if its Maslov class vanishes.
scientific article; zbMATH DE number 2116891
scientific article