2018/03/23 by Gorodski, Claudio, Mendes, Ricardo A. E., Radeschi, Marco
#49Q05 (Primary) #53A10 #53C35 #53C40 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1803.08735
We find many examples of compact Riemannian manifolds (M,g) whose closed minimal hypersurfaces satisfy a lower bound on their index that is linear in their first Betti number. Moreover, we show that these bounds remain valid when the metric g is replaced with g' in a neighbourhood of g. Our examples (M,g) consist of certain minimal isoparametric hypersurfaces of spheres; their focal manifolds; the Lie groups SU(n) for n≤ 17, and Sp(n) for all n; and all quaternionic Grassmannians.