Schoen-Yau-Gromov-Lawson theory and isoparametric foliations

TL;DR

This paper constructs a double manifold with positive scalar curvature from a minimal isoparametric hypersurface in the sphere, using surgery theory, K-theory, and Clifford algebra representations to analyze its topology and foliation structure.

Contribution

It introduces a novel construction of double manifolds with positive scalar curvature linked to isoparametric hypersurfaces, extending surgery theory and topological analysis methods.

Findings

Constructed double manifolds with positive scalar curvature

Determined isotropy subgroups for homogeneous cases

Connected isoparametric foliations with scalar curvature properties

Abstract

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.