Killing vector field

<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a Killing vector field (often called a Killing field), named after <a href="/facts/Wilhelm_Killing/W27PB2MJ">Wilhelm Killing</a>, is a <a href="/facts/Vector_field/ccFNuPPp">vector field</a> on a <a href="/facts/Pseudo-Riemannian_manifold/VFXsVjqb">pseudo-Riemannian manifold</a> that preserves the <a href="/facts/Metric_tensor/tbqek1gJ">metric tensor</a>.  Killing vector fields are the <a href="/facts/Lie_group/a9jCQyjF">infinitesimal generators</a> of <a href="/facts/Isometry/K5wX8ah6">isometries</a>; that is, <a href="/facts/Flow_(geometry)/CrmJPfeV">flows</a> generated by Killing vector fields are <a href="/facts/Isometry_(Riemannian_geometry)/K5wX8ah6">continuous isometries</a> of the <a href="/facts/Manifold/rXPERJtu">manifold</a>. This means that the flow generates a <a href="/facts/Symmetry_in_mathematics/KtLgoqyX">symmetry</a>, in the sense that moving each point of an object the same distance in the direction of the <i>Killing vector</i> will not distort distances on the object.
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Killing vector field open-in-new

Killing vector field