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Research Article Open access CC BY 4.0

Geodesically Complete Lie Algebroid

Mahamane Saminou Ali, Mouhamadou Hassirou, Bazanfare Mahaman

Journal of Advances in Mathematics and Computer Science · pp. 1–12 · Published 15 Jun 2017

10.9734/BJMCS/2017/34009

Abstract

In this paper we introduce the notion of geodesically complete Lie algebroid. We give a Riemannian distance on the connected base manifold of a Riemannian Lie algebroid. We also prove that the distance is equivalent to natural one if the base manifold was endowed with Riemannian metric. We obtain Hopf Rinow type theorem in the case of transitive Riemannian Lie algebroid, and give a characterization of the connected base manifold of a geodesically complete Lie algebroid.

Lie algebroid Riemannian metric and distance geodesically complete structure

References (8)

  1. 1 Integrability of Lie brackets [DOI]
  2. 2 Geometric Models for Noncommutative Algebras
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  8. 8 On Almost Complex Lie Algebroids [DOI]

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