On Geometry and Symmetry of Kepler Systems. I
@article{Zhou2017OnGA,
title={On Geometry and Symmetry of Kepler Systems. I},
author={Jian Zhou},
journal={arXiv: Mathematical Physics},
year={2017}
}We study the Kepler metrics on Kepler manifolds from the point of view of Sasakian geometry and Hessian geometry. This establishes a link between the problem of classical gravity and the modern geometric methods in the study of AdS/CFT correspondence in string theory.
5 Citations
Hessian Geometry and Phase Change of Gibbons-Hawking Metrics
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Hessian Geometry and Phase Changes of Multi-Taub-NUT Metrics
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We study the Hessian geometry of toric multi-Taub-NUT metrics and their phase change phenomena via the images of their moment maps. This generalizes an earlier paper on toric Gibbons-Hawking metrics.
Phase Transition of Kähler–Einstein Metrics via Moment Maps
- MathematicsCommunications in Mathematics and Statistics
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We study the phase transition of Kähler Ricci-flat metrics on some open Calabi–Yau spaces with the help of the images of moment maps of natural torus actions on these spaces.
Phase Transition of Kähler–Einstein Metrics via Moment Maps
- MathematicsCommunications in Mathematics and Statistics
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We study the phase transition of Kähler Ricci-flat metrics on some open Calabi–Yau spaces with the help of the images of moment maps of natural torus actions on these spaces.
Noncommutative Kepler Dynamics: symmetry groups and bi-Hamiltonian structures
- Physics, MathematicsTheoretical and Mathematical Physics
- 2021
Integrals of motion are constructed from noncommutative (NC ) Kepler dynamics, generating \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}…
References
SHOWING 1-10 OF 50 REFERENCES
On the Geometry of the Kepler Problem
- Physics, Mathematics
- 1983
It will be convenient to use the term Kepler orbit for any curve x = x(t) in 3-space which arises as a solution to the Newtonian two body problem. Hamilton showed that the velocity vector v = dx/dt...
On the Regularization of the Kepler Problem
- Physics, Mathematics
- 2010
We show that for the Kepler problem the canonical Ligon-Schaaf regularization map can be understood in a straightforward manner as an adaptation of the Moser regularization. In turn this explains the…
The Kepler problem and geodesic flows in spaces of constant curvature
- Mathematics, Physics
- 1977
The main result of this paper is a theorem on the trajectory equivalence of phase flows on isoenergetic surfaces with a positive energy level in the Kepler problem and perturbed kepler problem. The…
Variations on a Theme by Kepler
- Mathematics
- 1990
A series of five lectures exploring the role that groups, especially Lie groups, play in revealing the laws of nature, focusing on the ramifications and expansion of several of Kepler's laws. About…
Sasaki-Einstein Manifolds
- Mathematics
- 2010
This article is an overview of some of the remarkable progress that has been made in Sasaki-Einstein geometry over the last decade, which includes a number of new methods of constructing…
Rotationally symmetric pseudo-Kähler metrics of constant scalar curvatures
- Mathematics
- 2011
We study the ordinary differential equations related to rotationally symmetric pseudo-Kähler metrics of constant scalar curvatures. We present various solutions on various holomorphic line bundles…
Special Lagrangian fibrations, wall-crossing, and mirror symmetry
- Mathematics
- 2008
In this survey paper, we briefly review various aspects of the SYZ approach to mirror symmetry for non-Calabi-Yau varieties, focusing in particular on Lagrangian fibrations and wall-crossing…