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# Communications in Analysis and Geometry

## Volume 20 (2012)

### Number 5

### Schoen–Yau–Gromov–Lawson theory and isoparametric foliations

Pages: 989 – 1018

DOI: http://dx.doi.org/10.4310/CAG.2012.v20.n5.a4

#### Authors

#### 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.

Published 9 April 2013