English

On weak holonomy

Differential Geometry 2007-05-23 v2

Abstract

We prove that SU(n) (n > 2) and Sp(n)U(1) (n > 1) are the only connected Lie groups acting transitively and effectively on some sphere which can be weak holonomy groups of a Riemannian manifold without having to contain its holonomy group. In both cases the manifold is Kaehler.

Cite

@article{arxiv.math/0403479,
  title  = {On weak holonomy},
  author = {Bogdan Alexandrov},
  journal= {arXiv preprint arXiv:math/0403479},
  year   = {2007}
}

Comments

17 pages, LATEX; two references added