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SubRiemannian Geometry on the Sphere 𝕊3

Published online by Cambridge University Press:  20 November 2018

Ovidiu Calin ,
Der-Chen Chang  and
Irina Markina
Ovidiu Calin
Affiliation:
Department of Mathematics, Eastern Michigan University, Ypsilanti, MI, 48197, U.S.A. e-mail: ocalin@emich.edu
Der-Chen Chang
Affiliation:
Department of Mathematics, Georgetown University, Washington, D.C., 20057, U.S.A. and National Centre for Theoretical Sciences, Mathematics Division, National Tsing Hua University, Hsinchu, 30013, Taiwan, ROC e-mail: chang@georgetown.edu
Irina Markina
Affiliation:
Department of Mathematics, University of Bergen, Johannes Brunsgate 12, Bergen 5008, Norway e-mail: irina.markina@uib.no
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Abstract

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We discuss the subRiemannian geometry induced by two noncommutative vector fields which are left invariant on the Lie group ${{\mathbb{S}}^{3}}$.

Keywords

53C1753C2235H20noncommutative Lie groupquaternion groupsubRiemannian geodesichorizontal distributionconnectivity theoremholonomic constraint
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 61 , Issue 4 , 01 August 2009 , pp. 721 - 739
Copyright
Copyright © Canadian Mathematical Society 2012

References

[1] Beals, R., Gaveau, B., and Greiner, P. C.. On a geometric formula for the fundamental solution of subelliptic Laplacians. Math. Nachr. 181(1996), 81–163.Google Scholar
[2] Beals, R., Gaveau, B., and Greiner, P. C., Complex Hamiltonian mechanics and parametrices for subelliptic Laplacians. I, II, III. Bull. Sci. Math. 21(1997), no. 1, 1–36, no. 2, 97–149, no. 3, 195–259.Google Scholar
[3] Beals, R., Gaveau, B., and Greiner, P. C., Hamilton-Jacobi theory and the heat kernel on Heisenberg groups. J. Math. Pures Appl. 79(2000), no. 7, 633–689.Google Scholar
[4] Beals, R. and Greiner, P. C.: Calculus on Heisenberg Manifolds. Annals of Mathematics Studies 119. Princeton University Press, Princeton, NJ, 1988.Google Scholar
[5] Calin, O., Chang, D.-C. and Greiner, P. C., Geometric Analysis on the Heisenberg group and Its Generalizations. A MS/IP Studies in Advanced Mathematics 40, International Press, Somerville, MA, 2007.Google Scholar
[6] Calin, O., D.-C., Chang and Greiner, P. C., Geometric mechanics on the Heisenberg group. Bull. Inst. Math. Acad. Sinica 33(2005), no. 3, 185–252.Google Scholar
[7] Chang, D.-C. and Markina, I., Geometric analysis on quaternion H-type groups. J. Geom. Anal. 16(2006), no. 2, 265–294.Google Scholar
[8] Chow, W.-L.. Über Systeme von linearen partiellen Differentialgleichungen erster Ordnung. Math. Ann. 117(1939), 98–105.Google Scholar
[9] Gaveau, B., Principe de moindre action, propagation de la chaleur et estimées souselliptiques sur certains groupes nilpotent. Acta Math. 139(1977), 95–153.Google Scholar
[10] Strichartz, R.. Sub-Riemannian geometry. J. Differential Geom. 24(1986), no. 2, 221–263.Google Scholar