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An Implementation Method for the Geodesics with Constraints on Heisenberg Manifolds

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DOI: 10.4236/am.2012.330209    3,154 Downloads   5,190 Views  

ABSTRACT

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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.

References

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[3] D.-C. Chang, I. Markina and A. Vasil’ev, “Sub-Riemannian Geodesics on the 3-D Sphere,”2008. http://arxiv.org/pdf/0804.1695.pdf
[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.
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[6] O. Calin, “The Missing Direction and Differential Geometry on Heisenberg Manifolds,” Ph.D. Thesis, Toronto University, Toronto, 2000.

  
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