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Geodesics in a Manifold with Heisenberg Group as Boundary

Published online by Cambridge University Press:  20 November 2018

Yilong Ni
Yilong Ni*
Affiliation:
Department of Mathematics and Statistics, McMaster University, 1280 Main StreetWest, Hamilton, ON, L8S 4K1 e-mail: [email protected]
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Abstract

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The Heisenberg group is considered as the boundary of a manifold. A class of hypersurfaces in this manifold can be regarded as copies of the Heisenberg group. The properties of geodesics in the interior and on the hypersurfaces are worked out in detail. These properties are strongly related to those of the Heisenberg group.

Keywords

53C2253C17Heisenberg groupHamiltonian mechanicsgeodesic
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 56 , Issue 3 , 01 June 2004 , pp. 566 - 589
Copyright
Copyright © Canadian Mathematical Society 2004

References

[1] Beals, R., Geometry and PDE on the Heisenberg group: a case study. In: The geometrical study of differential equations (Washington, DC, 2000), Contemp. Math., 285, Amer.Math. Soc., Providence, RI, pp. 21–27.Google Scholar
[2] Beals, R., Gaveau, B. and Greiner, P. C., Hamilton-Jacobi theory and the heat kernel on Heisenberg groups. J. Math. Pures Appl. (7) 79(2000), 633–689.Google Scholar
[3] Gaveau, B., Principe de moindre action, propagation de la chaleur et estimées sous-elliptiques sur certains groupes nilpotents. Acta Math. 139(1977), 95–153.Google Scholar
[4] Gaveau, B., Systèmes dynamiques associés a certains operateurs hypoelliptiques. Bull. Sci. Math. 102(1978), 203–229.Google Scholar
[5] Strichartz, R., Sub-Riemannian geometry. J. Differential Geom. 24(1986), 221–263; correction, ibid. 30(1989), 595–596.Google Scholar