Cones over Pseudo – Riemannian Manifolds and their Holonomy

  title={Cones over Pseudo – Riemannian Manifolds and their Holonomy},
  author={D. V. Alekseevsky and Vicente Cort{\'e}s and Anton S. Galaev and Thomas Leistner},
By a classical theorem of Gallot (1979), a Riemannian cone over a complete Riemannian manifold is either flat or has irreducible holonomy. We consider metric cones with reducible holonomy over pseudo-Riemannian manifolds. First we describe the local structure of the base of the cone when the holonomy of the cone is decomposable. For instance, we find that the holonomy algebra of the base is always the full pseudo-orthogonal Lie algebra. One of the global results is that a cone over a compact… CONTINUE READING
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