Semi - Riemannian Geometry with Nonholonomic Constraints

Details Semi - Riemannian Geometry with Nonholonomic Constraints Semi - Riemannian Geometry with Nonholonomic Constraints

2009-01-11

arxiv.org/abs/0901.1477v1

Mathematics

Differential Geometry

Scientific paper

In the present article the geometry of semi-Riemannian manifolds with nonholonomic constraints is studied. These manifolds can be considered as analogues to the sub-Riemannian manifolds, where the positively definite metric is substituted by a nondegenerate metric. To study properties of the exponential map the Christoffel symbols and other differential operators were introduced. We study solutions of the Hamiltonian system and their projections into the underlying manifold. The explicit formulae were found for a specific example of a semi-Riemannian manifold with nonholonomic constraints.

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