Geodesically Complete Lie Algebroid
Mahamane Saminou Ali
Université d'Agadez, FS, Agadez, Niger.
Mouhamadou Hassirou *
Université Abdou Moumouni, FAST, Niamey, Niger.
Bazanfare Mahaman
Université Abdou Moumouni, FAST, Niamey, Niger.
*Author to whom correspondence should be addressed.
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.
Keywords: Lie algebroid, Riemannian metric and distance, geodesically complete structure