scholarly journals Erratum to: A note on the Kepler problem in a space of constant curvature

1990 ◽  
Vol 105 (6) ◽  
pp. 707-707
Author(s):  
N. Katayama
Keyword(s):  
Constant Curvature ◽  
Kepler Problem ◽  
Space Of Constant Curvature

scholarly journals Lambert's theorem and projective dynamics

2019 ◽  
Vol 377 (2158) ◽  
pp. 20180417
Author(s):  
Alain Albouy ◽  
Lei Zhao
Keyword(s):  
Constant Curvature ◽  
Vortex Dynamics ◽  
Kepler Problem ◽  
Keplerian Orbit ◽  
Theme Issue ◽  
Spaces Of Constant Curvature ◽  
Elapsed Time ◽  
Space Of Constant Curvature

We prove that the classical Lambert theorem about the elapsed time on an arc of Keplerian orbit extends without change to the Kepler problem on a space of constant curvature. We prove that the Hooke problem has a property similar to Lambert's theorem, which also extends to the spaces of constant curvature. This article is part of the theme issue ‘Topological and geometrical aspects of mass and vortex dynamics’.

scholarly journals Kinematic formula and tube formula in space of constant curvature

1990 ◽  
Vol 33 (1) ◽  
pp. 79-88
Author(s):  
Sungyun Lee
Keyword(s):  
Euclidean Space ◽  
Euler Characteristic ◽  
Constant Curvature ◽  
Kinematic Formula ◽  
Curvature Invariants ◽  
Space Of Constant Curvature

The Euler characteristic of an even dimensional submanifold in a space of constant curvature is given in terms of Weyl's curvature invariants. A derivation of Chern's kinematic formula in non-Euclidean space is completed. As an application of above results Weyl's tube formula about an odd-dimensional submanifold in a space of constant curvature is obtained.

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