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SubRiemannian geometry on the sphere
Ovidiu Calin, Der-Chen Chang, Irina Markina
The present paper starts with an introduction to quaternions and then defines the 3-dimmensional sphere as the set of quaternions of length one. The quaternion group induces on $\m…
Modified action and differential operators on the 3-D sub-Riemannian sphere
Der-Chen Chang, Irina Markina, Alexander Vasil'ev
Our main aim is to present a geometrically meaningful formula for the fundamental solutions to a second order sub-elliptic differential equation and to the heat equation associated…
Sub-Riemannian geodesics on the 3-D sphere
Der-Chen Chang, Irina Markina, Alexander Vasil'ev
The unit sphere can be identified with the unitary group SU(2). Under this identification the unit sphere can be considered as a non-commutative Lie group. The commut…
Sub-Lorentzian Geometry on Anti-De Sitter Space
Der-Chen Chang, Irina Markina, Alexander Vasil'ev
Sub-Riemannian Geometry is proved to play an important role in many applications, e.g., Mathematical Physics and Control Theory. The simplest example of sub-Riemannian structure is…