Manifolds admitting a metric with co-index of symmetry 4

Abstract

By a recent result, it is known that compact homogeneous spaces with co-index of symmetry 4 are quotients of a semisimple Lie group of dimension at most 10. In this paper we determine exactly which ones of these spaces actually admit such a metric. For all the admissible spaces we construct explicit examples of these metrics.

arXiv comment10 pages. We add Theorem 4.1 and an appendix on strongly symmetric autoparallel distributions