Communications in Analysis and Geometry
Volume 20 (2012)
Schoen–Yau–Gromov–Lawson theory and isoparametric foliations
Pages: 989 – 1018
Motivated by the celebrated Schoen–Yau–Gromov–Lawson surgery theory on metrics of positive scalar curvature, we construct a double manifold associated with a minimal isoparametric hypersurface in the unit sphere. The resulting double manifold carries a metric of positive scalar curvature and an isoparametric foliation as well. To investigate the topology of the double manifolds, we use $K$-theory and the representation of the Clifford algebra for the FKM-type, and determine completely the isotropy subgroups of singular orbits for homogeneous case.