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A note on Riemannian connections with skew torsion and the de Rham splitting

A note on Riemannian connections with skew torsion and the de Rham splitting We prove that a Riemannian manifold admitting a metric connection with totally skew-symmetric torsion and reducible holonomy is locally reducible, provided it has nonpositive sectional curvature. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Manuscripta Mathematica Springer Journals

A note on Riemannian connections with skew torsion and the de Rham splitting

Dileo, G.; Lotta, A.
Manuscripta Mathematica , Volume 156 (4) – Aug 21, 2017
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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer-Verlag GmbH Germany
Subject
Mathematics; Mathematics, general; Algebraic Geometry; Topological Groups, Lie Groups; Geometry; Number Theory; Calculus of Variations and Optimal Control; Optimization
ISSN
0025-2611
eISSN
1432-1785
DOI
10.1007/s00229-017-0967-y
Publisher site
See Article on Publisher Site

Abstract

We prove that a Riemannian manifold admitting a metric connection with totally skew-symmetric torsion and reducible holonomy is locally reducible, provided it has nonpositive sectional curvature.

Journal

Manuscripta Mathematica – Springer Journals

Published: Aug 21, 2017

References

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    Agricola, I; Friedrich, T
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    Nagy, PA
  • Foliations on Riemannian Manifolds and Submanifolds
    Rovenskii, YV
  • A remark on locally homogeneous Riemannian spaces
    Spiro, A
  • Locally homogeneous Riemannian manifolds, Differential geometry (Turin, 1992)
    Tricerri, F
  • Homogeneous Structures on Riemannian Manifolds, London Mathematical Society Lecture Note Series 83
    Tricerri, F; Vanhecke, L