Faithful representation

From formulasearchengine
Revision as of 09:42, 3 April 2010 by en>Tobias Bergemann (→‎Properties: Minor rewording, moved complex LaTeX expression out of line)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search

In conformal geometry, the conformal Killing equation on a manifold of space-dimension n with metric describes those vector fields which preserve up to scale, i.e.

for some function (where is the Lie derivative). Vector fields that satisfy the conformal Killing equation are exactly those vector fields whose flow preserves the conformal structure of the manifold. The name Killing refers to Wilhelm Killing, who first investigated the Killing equation for vector fields that preserve a Riemannian metric.

By taking the trace we find that necessarily . Therefore we can write the conformal Killing equation as

In abstract indices

where the round brackets denote symmetrization.

See also

Notes

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.


Template:Differential-geometry-stub