2019
Том 71
№ 2

All Issues

Romanov S. S.

Articles: 2
Brief Communications (Russian)

Piecewise-maximum closed Geodesic trajectories on bounded Toroidal manifolds

Romanov S. S.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 8. - pp. 1139–1142

We use toroidal coordinates for the investigation of maximum geodesic trajectories for arbitrary parameters of a torus. Conditions under which trajectories are located in a bounded part of the toroidal manifold are considered. Using global invariants, we construct closed piecewise-maximum geodesic trajectories.

Brief Communications (Russian)

Plane Closed Trajectories on Certain Manifolds with Rotation Metric

Romanov S. S.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 2. - pp. 276-283

Trajectories on spherical and toroidal manifolds are studied by methods of infinitesimal and global geometry.