location:  Publications → journals
Search results

Search: All articles in the CJM digital archive with keyword geodesic

 Expand all        Collapse all Results 1 - 4 of 4

1. CJM 2012 (vol 66 pp. 760)

Hu, Shengda; Santoprete, Manuele
 Regularization of the Kepler Problem on the Three-sphere In this paper we regularize the Kepler problem on $S^3$ in several different ways. First, we perform a Moser-type regularization. Then, we adapt the Ligon-Schaaf regularization to our problem. Finally, we show that the Moser regularization and the Ligon-Schaaf map we obtained can be understood as the composition of the corresponding maps for the Kepler problem in Euclidean space and the gnomonic transformation. Keywords:Kepler problem on the sphere, Ligon-Shaaf regularization, geodesic flow on the sphereCategory:70Fxx

2. 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

3. CJM 2004 (vol 56 pp. 776)

Lim, Yongdo
 Best Approximation in Riemannian Geodesic Submanifolds of Positive Definite Matrices We explicitly describe the best approximation in geodesic submanifolds of positive definite matrices obtained from involutive congruence transformations on the Cartan-Hadamard manifold ${\mathrm{Sym}}(n,{\Bbb R})^{++}$ of positive definite matrices. An explicit calculation for the minimal distance function from the geodesic submanifold ${\mathrm{Sym}}(p,{\mathbb R})^{++}\times {\mathrm{Sym}}(q,{\mathbb R})^{++}$ block diagonally embedded in ${\mathrm{Sym}}(n,{\mathbb R})^{++}$ is given in terms of metric and spectral geometric means, Cayley transform, and Schur complements of positive definite matrices when $p\leq 2$ or $q\leq 2.$ Keywords:Matrix approximation, positive, definite matrix, geodesic submanifold, Cartan-Hadamard manifold,, best approximation, minimal distance function, global tubular, neighborhood theorem, Schur complement, metric and spectral, geometric mean, Cayley transformCategories:15A48, 49R50, 15A18, 53C3

4. 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