Communications in Analysis and Geometry

Volume 20 (2012)

Number 5

Schoen–Yau–Gromov–Lawson theory and isoparametric foliations

Pages: 989 – 1018

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

Authors

Zizhou Tang (Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing, China)

Yuquan Xie (School of Mathematical Sciences, Peking University, Beijing, China)

Wenjiao Yan (Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing, China)

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