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Was (wer) ist hyperbolic$36650$ - definition
SPACE WHERE EVERY POINT LOCALLY RESEMBLES A HYPERBOLIC SPACE
Hyperbolic n-manifold; Hyperbolic manifolds; Hyperbolic metric
![The [[Pseudosphere]]. Each half of this shape is a hyperbolic 2-manifold (i.e. surface) with boundary.](https://commons.wikimedia.org/wiki/Special:FilePath/The Pseudosphere.jpg?width=200 "The [[Pseudosphere]]. Each half of this shape is a hyperbolic 2-manifold (i.e. surface) with boundary.")
Hyperbolic trajectory
![gravitational potential well]] of the central mass shows potential energy, and the kinetic energy of the hyperbolic trajectory is shown in red. The height of the kinetic energy decreases as the speed decreases and distance increases according to Kepler's laws. The part of the kinetic energy that remains above zero total energy is that associated with the hyperbolic excess velocity.](https://commons.wikimedia.org/wiki/Special:FilePath/Gravity Wells Potential Plus Kinetic Energy - Circle-Ellipse-Parabola-Hyperbola.png?width=200 "gravitational potential well]] of the central mass shows potential energy, and the kinetic energy of the hyperbolic trajectory is shown in red. The height of the kinetic energy decreases as the speed decreases and distance increases according to Kepler's laws. The part of the kinetic energy that remains above zero total energy is that associated with the hyperbolic excess velocity.")
TRAJECTORY OF ANY OBJECT AROUND A CENTRAL BODY WITH MORE THAN ENOUGH SPEED TO ESCAPE THE CENTRAL OBJECT'S GRAVITATIONAL PULL
Hyperbolic orbit; Hyperbolic Orbit; Hyperbolic excess velocity; Radial hyperbolic trajectory; Radial hyperbolic orbit
In astrodynamics or celestial mechanics, a hyperbolic trajectory is the trajectory of any object around a central body with more than enough speed to escape the central object's gravitational pull. The name derives from the fact that according to Newtonian theory such an orbit has the shape of a hyperbola.
Hyperbolic space
HOMOGENEOUS SPACE THAT HAS A CONSTANT NEGATIVE CURVATURE (NOT ANY HYPERBOLIC MANIFOLD)
Hyperbolic 3-space; Real hyperbolic space; Hyperbolic Space; Hyperbolic spaces; Hyperbolic Spaces; H^n
In mathematics, hyperbolic space of dimension n is the unique simply connected, n-dimensional Riemannian manifold of constant sectional curvature equal to -1. It is homogeneous, and satisfies the stronger property of being a symmetric space.
Hyperbolic link
![4<sub>1</sub> knot]]](https://commons.wikimedia.org/wiki/Special:FilePath/Blue Figure-Eight Knot.png?width=200 "4<sub>1</sub> knot]]")
![[[Borromean rings]] are a hyperbolic link.](https://commons.wikimedia.org/wiki/Special:FilePath/BorromeanRings.svg?width=200 "[[Borromean rings]] are a hyperbolic link.")
TYPE OF MATHEMATICAL LINK
Hyperbolic knot
In mathematics, a hyperbolic link is a link in the 3-sphere with complement that has a complete Riemannian metric of constant negative curvature, i.e.
Wikipedia
Hyperbolic manifold
In mathematics, a hyperbolic manifold is a space where every point looks locally like hyperbolic space of some dimension. They are especially studied in dimensions 2 and 3, where they are called hyperbolic surfaces and hyperbolic 3-manifolds, respectively. In these dimensions, they are important because most manifolds can be made into a hyperbolic manifold by a homeomorphism. This is a consequence of the uniformization theorem for surfaces and the geometrization theorem for 3-manifolds proved by Perelman.
