Abstract
We construct some examples of ℍ-types Carnot groups related to quaternion numbers and study their geometric properties. We involve the Hamiltonian formalism to obtain the equations of geodesics and calculate the cardinality of geodesics joining two different points on these groups. We prove Kepler’s law and give a nice geometric interpretation of the length of geodesies.
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Communicated by Steven Krantz
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Chang, DC., Markina, I. Geometric analysis on quaternion ℍ-type groups. J Geom Anal 16, 265–294 (2006). https://doi.org/10.1007/BF02922116
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DOI: https://doi.org/10.1007/BF02922116