Isometries of complemented subRiemannian manifolds

2012/03/05 by Hladky, Robert K.
#53C17 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1203.1066

Abstract

We show that the group of smooth isometries of a complemented sub-Riemannian manifold form a Lie group and establish dimension estimates based on the torsion of the canonical connection. We explore the interaction of curvature and the structure of isometries and Killing fields and derive a Bochner formula for Killing fields. Sub-Riemannian generalizations of classical results of Bochner and Berger are established. We also apply our theory to common sub-categories of complemented sub-Riemannian geometries and show how to compute the isometry groups for several examples, including SO(n), SL(n) and the rototranslation group.

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