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1. CJM 2009 (vol 61 pp. 721)
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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)
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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)
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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 |