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Search: MSC category 53C22 ( Geodesics [See also 58E10] )

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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 constraintCategories: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, geodesicCategories:53C22, 53C17

3. CJM 2003 (vol 55 pp. 1080)

Kellerhals, Ruth
 Quaternions and Some Global Properties of Hyperbolic $5$-Manifolds We provide an explicit thick and thin decomposition for oriented hyperbolic manifolds $M$ of dimension $5$. The result implies improved universal lower bounds for the volume $\rmvol_5(M)$ and, for $M$ compact, new estimates relating the injectivity radius and the diameter of $M$ with $\rmvol_5(M)$. The quantification of the thin part is based upon the identification of the isometry group of the universal space by the matrix group $\PS_\Delta {\rm L} (2,\mathbb{H})$ of quaternionic $2\times 2$-matrices with Dieudonn\'e determinant $\Delta$ equal to $1$ and isolation properties of $\PS_\Delta {\rm L} (2,\mathbb{H})$. Categories:53C22, 53C25, 57N16, 57S30, 51N30, 20G20, 22E40

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