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]
^Exact Solutions of Einstein's Field Equations. Cambridge University Press. 2003. pp. 163. ISBN 978-0-521-46136-8.
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dilation Homothetic center HomotheticvectorfieldHomothetic preferences This disambiguation page lists articles associated with the title Homothetic. If...
vectorfields is isomorphic to the Lie algebra g {\displaystyle {\mathfrak {g}}} of G. Affine vectorfield Curvature collineation Homotheticvector field...
{\frac {1}{2}}n(n+1)+1} . A homotheticvectorfield is uniquely determined by specifying the values of the vectorfield and its first covariant derivative...
Killing vectorfields find extensive applications (including in classical mechanics) and are related to conservation laws. A homotheticvectorfield is one...
Charles P. Boyer and Krzysztof Galicki and their co-authors. The homotheticvectorfield on the cone over a Sasakian manifold is defined to be t ∂ / ∂ t...
infinite-dimensional. Every affine vectorfield is a curvature collineation. Conformal vectorfieldHomotheticvectorfield Killing vectorfield Matter collineation...
electric and magnetic fields. Affine vector field Conformal vector field Curvature collineation Homotheticvectorfield Spacetime symmetries v t e v t e...
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...
0-homogeneous functions, that is, the functions that are invariant by homothetic rescaling, or "independent of the radial coordinate". A function (defined...
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...
g)} is called a Ricci soliton if, and only if, there exists a smooth vectorfield V {\displaystyle V} such that Ric ( g ) = λ g − 1 2 L V g , {\displaystyle...
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...
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...
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...
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...