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Search: MSC category 53C17 ( Sub-Riemannian geometry )

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1. CJM 2009 (vol 61 pp. 721)

Calin, Ovidiu; Chang, Der-Chen; Markina, Irina
SubRiemannian Geometry on the Sphere $\mathbb{S}^3$
We discuss the subRiemannian geometry induced by two noncommutative vector fields which are left invariant on the Lie group $\mathbb{S}^3$.

Keywords:noncommutative Lie group, quaternion group, subRiemannian geodesic, horizontal distribution, connectivity theorem, holonomic constraint
Categories:53C17, 53C22, 35H20

2. CJM 2004 (vol 56 pp. 566)

Ni, Yilong
Geodesics in a Manifold with Heisenberg Group as Boundary
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:Heisenberg group, Hamiltonian mechanics, geodesic
Categories:53C22, 53C17

3. CJM 2004 (vol 56 pp. 590)

Ni, Yilong
The Heat Kernel and Green's Function on a Manifold with Heisenberg Group as Boundary
We study the Riemannian Laplace-Beltrami operator $L$ on a Riemannian manifold with Heisenberg group $H_1$ as boundary. We calculate the heat kernel and Green's function for $L$, and give global and small time estimates of the heat kernel. A class of hypersurfaces in this manifold can be regarded as approximations of $H_1$. We also restrict $L$ to each hypersurface and calculate the corresponding heat kernel and Green's function. We will see that the heat kernel and Green's function converge to the heat kernel and Green's function on the boundary.

Categories:35H20, 58J99, 53C17

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