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Isometries of complemented subRiemannian manifolds
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 f...
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Published in: | arXiv.org 2013-01 |
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Main Author: | |
Format: | Article |
Language: | English |
Subjects: | |
Online Access: | Get full text |
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Summary: | 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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ISSN: | 2331-8422 |