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Homothetic vector field information


In physics, a homothetic vector field (sometimes homothetic collineation or homothety) is a projective vector field which satisfies the condition:

where c is a real constant. Homothetic vector fields find application in the study of singularities in general relativity. They can also be used to generate new solutions for Einstein equations by similarity reduction.[1]

  1. ^ Exact Solutions of Einstein's Field Equations. Cambridge University Press. 2003. pp. 163. ISBN 978-0-521-46136-8.

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Homothetic vector field

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In physics, a homothetic vector field (sometimes homothetic collineation or homothety) is a projective vector field which satisfies the condition: L X...

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Homothetic

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dilation Homothetic center Homothetic vector field Homothetic preferences This disambiguation page lists articles associated with the title Homothetic. If...

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Killing vector field

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vector fields is isomorphic to the Lie algebra g {\displaystyle {\mathfrak {g}}} of G. Affine vector field Curvature collineation Homothetic vector field...

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Projective vector field

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{\frac {1}{2}}n(n+1)+1} . A homothetic vector field is uniquely determined by specifying the values of the vector field and its first covariant derivative...

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Affine vector field

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{L}}_{X}g_{ab})_{;c}=0} Conformal vector field Curvature collineation Homothetic vector field Killing vector field Matter collineation Spacetime symmetries...

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Conformal Killing vector field

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vector field Conformal Killing tensor Curvature collineation Einstein manifold Homothetic vector field Invariant differential operator Killing vector...

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Spacetime symmetries

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Killing vector fields find extensive applications (including in classical mechanics) and are related to conservation laws. A homothetic vector field is one...

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Sasakian manifold

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Charles P. Boyer and Krzysztof Galicki and their co-authors. The homothetic vector field on the cone over a Sasakian manifold is defined to be t ∂ / ∂ t...

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Curvature collineation

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infinite-dimensional. Every affine vector field is a curvature collineation. Conformal vector field Homothetic vector field Killing vector field Matter collineation...

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Matter collineation

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electric and magnetic fields. Affine vector field Conformal vector field Curvature collineation Homothetic vector field Spacetime symmetries v t e v t e...

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Outline of geometry

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Stereometry Ball Convex Convex hull Coxeter group Euclidean distance Homothetic center Hyperplane Lattice Ehrhart polynomial Leech lattice Minkowski's...

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Gorman polar form

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Gorman form. Particularly: linear, Leontief and Cobb-Douglas utilities are homothetic and thus have the Gorman form. To prove that the Engel curves of a function...

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Euler sequence

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0-homogeneous functions, that is, the functions that are invariant by homothetic rescaling, or "independent of the radial coordinate". A function (defined...

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Convex set

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interior is non-empty). We can inscribe a rectangle r in C such that a homothetic copy R of r is circumscribed about C. The positive homothety ratio is...

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Ricci soliton

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g)} is called a Ricci soliton if, and only if, there exists a smooth vector field V {\displaystyle V} such that Ric ⁡ ( g ) = λ g − 1 2 L V g , {\displaystyle...

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List of convexity topics

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n-dimensional Euclidean space can be covered by 2n or fewer smaller bodies homothetic with the original body. Hadwiger's theorem - a theorem that characterizes...

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Problem of Apollonius

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and of Joseph Diaz Gergonne (1814). Whereas Poncelet's proof relies on homothetic centers of circles and the power of a point theorem, Gergonne's method...

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Hyperbolic geometry

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interval on a ray is given by logarithmic measure so it is invariant under a homothetic transformation ( x , y ) ↦ ( λ x , λ y ) , λ > 0. {\displaystyle (x,y)\mapsto...

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Charles Loewner

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boundary case of equality is attained if and only if the metric is flat and homothetic to the so-called equilateral torus, i.e. torus whose group of deck transformations...

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