The Experts below are selected from a list of 312 Experts worldwide ranked by ideXlab platform
Cezary Gonera - One of the best experts on this subject based on the ideXlab platform.
-
New superintegrable models on spaces of Constant Curvature
Annals of Physics, 2020Co-Authors: Cezary Gonera, Joanna GoneraAbstract:Abstract A general class of superintegrable systems on 2D spaces of Constant Curvature is known for which the potential is not spherically symmetric but allows separation of variables in (geodesic) polar coordinates. The radial parts of these potentials correspond either to an isotropic harmonic oscillator or a generalized Kepler potential. Unlike the radial parts, the angular ones are given implicitly. In the present paper new two-parameter families of angular potentials are constructed in terms of elementary functions. It is shown that for appropriate choice of parameters a family corresponding to the oscillator or Kepler type radial potential reduces to the Poschl–Teller potential. This allows considering Hamiltonian systems defined by this family as generalizations of Tremblay–Turbiner–Winternitz (TTW) or Post–Winternitz (PW) models, both on the plane and on curved spaces of Constant Curvature.
-
Superintegrable systems on spaces of Constant Curvature
Annals of Physics, 2014Co-Authors: Cezary Gonera, Magdalena KaszubskaAbstract:Abstract Construction and classification of two-dimensional (2D) superintegrable systems (i.e. systems admitting, in addition to two global integrals of motion guaranteeing the Liouville integrability, the third global and independent one) defined on 2D spaces of Constant Curvature and separable in the so-called geodesic polar coordinates are presented. The method proposed is applicable to any value of Curvature including the case of Euclidean plane, sphere and hyperbolic plane. The main result is a generalization of Bertrand’s theorem on 2D spaces of Constant Curvature and covers most of the known separable and superintegrable models on such spaces (in particular, the so-called Tremblay–Turbiner–Winternitz (TTW) and Post–Winternitz (PW) models which have recently attracted some interest).
Helmut Reckziegel - One of the best experts on this subject based on the ideXlab platform.
-
Hypersurfaces with Parallel Ricci Tensor in Spaces of Constant Curvature
Results in Mathematics, 1995Co-Authors: Helmut ReckziegelAbstract:Hypersurfaces with parallel Ricci tensor in spaces of Constant Curvature are classified. The main tool is a generalization of Moore’s decomposition theorem for isometric immersions.
Joanna Gonera - One of the best experts on this subject based on the ideXlab platform.
-
New superintegrable models on spaces of Constant Curvature
Annals of Physics, 2020Co-Authors: Cezary Gonera, Joanna GoneraAbstract:Abstract A general class of superintegrable systems on 2D spaces of Constant Curvature is known for which the potential is not spherically symmetric but allows separation of variables in (geodesic) polar coordinates. The radial parts of these potentials correspond either to an isotropic harmonic oscillator or a generalized Kepler potential. Unlike the radial parts, the angular ones are given implicitly. In the present paper new two-parameter families of angular potentials are constructed in terms of elementary functions. It is shown that for appropriate choice of parameters a family corresponding to the oscillator or Kepler type radial potential reduces to the Poschl–Teller potential. This allows considering Hamiltonian systems defined by this family as generalizations of Tremblay–Turbiner–Winternitz (TTW) or Post–Winternitz (PW) models, both on the plane and on curved spaces of Constant Curvature.
Magdalena Kaszubska - One of the best experts on this subject based on the ideXlab platform.
-
Superintegrable systems on spaces of Constant Curvature
Annals of Physics, 2014Co-Authors: Cezary Gonera, Magdalena KaszubskaAbstract:Abstract Construction and classification of two-dimensional (2D) superintegrable systems (i.e. systems admitting, in addition to two global integrals of motion guaranteeing the Liouville integrability, the third global and independent one) defined on 2D spaces of Constant Curvature and separable in the so-called geodesic polar coordinates are presented. The method proposed is applicable to any value of Curvature including the case of Euclidean plane, sphere and hyperbolic plane. The main result is a generalization of Bertrand’s theorem on 2D spaces of Constant Curvature and covers most of the known separable and superintegrable models on such spaces (in particular, the so-called Tremblay–Turbiner–Winternitz (TTW) and Post–Winternitz (PW) models which have recently attracted some interest).
Du Yan-hua - One of the best experts on this subject based on the ideXlab platform.
-
REMARKS ON FUJIWARA-BOL THEOREM IN A PLANE OF Constant Curvature
Journal of Mathematics, 2009Co-Authors: Du Yan-huaAbstract:In this paper we investigate the convex set in a plane of Constant Curvature. We follow Grinberg-Ren-Zhou’s idea and give a simplified proof of the well-known Fujiwara-Bol theorem in a plane of Constant Curvature.