Taiwanese Journal of Mathematics

Semi-Riemannian Geometry with Nonholonomic Constraints

Anna Korolko and Irina Markina

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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 positive definite metric is substituted by a nondegenerate metric. We study properties of the exponential map, the Christoffel symbols and other differential operators are 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.

Article information

Taiwanese J. Math., Volume 15, Number 4 (2011), 1581-1616.

First available in Project Euclid: 18 July 2017

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Zentralblatt MATH identifier

Primary: 53C50: Lorentz manifolds, manifolds with indefinite metrics 53B30: Lorentz metrics, indefinite metrics 53C17: Sub-Riemannian geometry

semi-Riemannian manifolds nondegenerate metric exponential map Christoffel symbol extremals quaternions


Korolko, Anna; Markina, Irina. Semi-Riemannian Geometry with Nonholonomic Constraints. Taiwanese J. Math. 15 (2011), no. 4, 1581--1616. doi:10.11650/twjm/1500406366. https://projecteuclid.org/euclid.twjm/1500406366

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