Communications in Analysis and Geometry

Volume 24 (2016)

Number 5

Introduction to the intrinsic rolling with indefinite metric

Pages: 1085 – 1106



Irina Markina (Department of Mathematics, University of Bergen, Norway)

Fátima Silva Leite (Department of Mathematics and Institute of Systems and Robotics, University of Coimbra, Portugal)


This paper concerns the rolling motion of one pseudo-Riemannian manifold over another. We compare the definition of rolling without slip and twist of two manifolds isometrically embedded into a pseudo-Euclidean space with the rolling defined only by intrinsic data, namely by metric tensors on manifolds. The smooth distribution on the configuration space, encoding the no-slip and no-twist kinematic conditions is constructed. Some results concerning the causal character of the rolling curves are also included. Several examples are presented along the paper to illustrate concepts and help to understand theoretical results.


pseudo-Riemannian manifolds, pseudo-Euclidean space, rolling map, Christoffel symbols

2010 Mathematics Subject Classification

37J60, 53A17, 53A35

Published 6 March 2017