Definition & Betydelse | Engelska ordet GEODESICS

Definition av GEODESICS

1. böjningsform av geodesic

Exempel på hur man kan använda GEODESICS i en mening

• In a Riemannian manifold or submanifold, geodesics are characterised by the property of having vanishing geodesic curvature.
• Meaning, they should form a 3-bundle of non-intersecting geodesics orthogonal to a series of spacelike hypersurfaces (hyperslices).
• Development of Riemannian geometry resulted in synthesis of diverse results concerning the geometry of surfaces and the behavior of geodesics on them, with techniques that can be applied to the study of differentiable manifolds of higher dimensions.
• If the covariant derivative is the Levi-Civita connection of a certain metric, then the geodesics for the connection are precisely those geodesics of the metric that are parametrised proportionally to their arc length.
• The Ricci tensor can be characterized by measurement of how a shape is deformed as one moves along geodesics in the space.
• This definition makes minimal surfaces a 2-dimensional analogue to geodesics, which are analogously defined as critical points of the length functional.
• If ∇ is a metric connection, then the affine geodesics are the usual geodesics of Riemannian geometry and are the locally distance minimizing curves.
• There are ways to cast de Sitter space with static coordinates (see de Sitter space), so unlike other FLRW models, de Sitter space can be thought of as a static solution to Einstein's equations even though the geodesics followed by observers necessarily diverge as expected from the expansion of physical spatial dimensions.
• They also provide a canonical example of Hopf fibration, where the geodesic flow induced by the linear fractional transformation decomposes complex projective space into stable and unstable manifolds, with the horocycles appearing perpendicular to the geodesics.
• It is also possible, if the thin shell is transparent to radiation, that gravastars may be distinguished from ordinary black holes by different gravitational lensing properties as null geodesics may pass through.
• The inertial trajectories of particles and radiation (geodesics) in the resulting geometry are then calculated using the geodesic equation.
• The projection is conformal, meaning that it preserves angles, and like the stereographic projection of the sphere it projects generalized circles (geodesics, hypercycles, horocycles, and circles) in the hyperbolic plane to generalized circles (lines or circles) in the plane.
• Algebraically, prime geodesics can be lifted to higher surfaces in much the same way that prime ideals in the ring of integers of a number field can be split (factored) in a Galois extension.
• The technical difficulty of their work is that geodesics in their infinite-dimensional context may have low differentiability.
• One side of the horizon contains closed space-like geodesics and the other side contains closed time-like geodesics.
• Since geodesics in HP are semicircles with centers on the boundary, the geodesics in Q are obtained from the correspondence and turn out to be rays from the origin or petal-shaped curves leaving and re-entering the origin.
• In summers and winters, the station functions as a base for research on geology, geodesics, geomorphology, glaciology, oceanology and biology.
• Schwarzschild geodesics pertain only to the motion of particles of masses so small they contribute little to the gravitational field.
• Analogously, the world lines of test particles in free fall are spacetime geodesics, the straightest possible lines in spacetime.
• This last equation signifies that the particle is moving along a timelike geodesic; massless particles like the photon instead follow null geodesics (replace −1 with zero on the right-hand side of the last equation).

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