Infinitesimal semisimple symplectic extrinsic symmetric spaces
We study infinitesimal semi-simple extrinsic symmetric spaces and give a classification in the symplectic case.
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arXiv subjects
Thomas Krantz
Publications and source records attributed to Thomas Krantz.
Canonical Torsion-Free Connections on the Total Space of the Tangent and the Cotangent Bundle
In this paper we define a class of torsion-free connections on the total space of the (co-)tangent bundle over a base-manifold with a connection and for which tangent spaces to the fibers are parallel. Each tangent space to a fiber is flat for these connections and the canonical projection from the (co-)tangent bundle to the base manifold is totally geodesic. In particular cases the connection is metric with signature (n,n) or symplectic and admits a single parallel totally isotropic tangent n-plane.
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On the Holonomy of Kaluza-Klein metrics
We investigate Kaluza-Klein metrics with a recurrent light-like vector field over a pseudo-Riemannian manifold.
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Holonomy representations which are a diagonal direct sum of two faithful representations
We study holonomy representations admitting a pair of supplementary faithful sub-representations. In particular the cases where the sub-representations are isomorphic respectively dual to each other are treated. In each case we have a closer look at the classification in small dimension.
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Representations admitting two pairs of supplementary invariant spaces
We examine the lattice generated by two pairs of supplementary vector subspaces of a finite-dimensional vector space by intersection and sum, with the aim of applying the results to the study of representations admitting two pairs of supplementary invariant spaces, or one pair and a reflexive form. We show that such a representation is a direct sum of three canonical sub-representations which we characterize. We then focus on holonomy representations with the same property.
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