An Implementation Method for the Geodesics with Constraints on Heisenberg Manifolds


In this paper we address the implementation issue of the geodesics method with constraints on Heisenberg manifolds. First we present more details on the method in order to facilitate its implementation and second we consider Mathema-tica as a software tool for the simulation. This implementation is of great importance since it allows easy and direct determination of Ricci tensor, which plays a fundamental role in the Heisenberg manifold metric.

Share and Cite:

Y. Khellaf and N. Bensalem, "An Implementation Method for the Geodesics with Constraints on Heisenberg Manifolds," Applied Mathematics, Vol. 3 No. 10A, 2012, pp. 1496-1504. doi: 10.4236/am.2012.330209.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] O. Calin and V. Mangione, “Geodesics with Constraints on Heisenberg Manifolds,” Results in Mathematics, 2003, pp. 44-53.
[2] M. Bonnefont, “Functional Inequality for Heat Kernels Sub-Elliptical,” Ph.D. Thesis, Paul Sabatier University, Toulouse, 2009.
[3] D.-C. Chang, I. Markina and A. Vasil’ev, “Sub-Riemannian Geodesics on the 3-D Sphere,”2008.
[4] L. Capogna, D. Danielli, S. Pauls and J. Tyson, “An Introduction to the Heisenberg Group and the Sub-Rie-mannian Isoperimetric Problem,” Die Deutsche Bibliothek, Deutsche Nationalbibliografie, 2007.
[5] R. Beals, B. Gaveau and P. C. Greiner, “Hamilton-Jacobi Theory and the Heat Kernel on Heisenberg Groups,” journal of mathéMatiques Pures et Appliquées, Vol. 79, No. 7, 2000, pp. 633-689. doi:10.1016/S0021-7824(00)00169-0
[6] O. Calin, “The Missing Direction and Differential Geometry on Heisenberg Manifolds,” Ph.D. Thesis, Toronto University, Toronto, 2000.

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.