Killing Symmetry
A Killing vector field is one of the most important types of symmetries and is defined to be a smooth vector field that preserves the metric tensor:
This is usually written in the expanded form as:
Killing vector fields find extensive applications (including in classical mechanics) and are related to conservation laws.
Read more about this topic: Spacetime Symmetries
Famous quotes containing the words killing and/or symmetry:
“Does he who loves someone on account of beauty really love that person? No, for smallpox, which will kill beauty without killing the person, will cause him to love the person no more. And if one loves me for my judgment, for my memory, he does not love me, for I can lose these qualities without losing myself. Where, then, is this myself, if it be neither in the body nor in the soul?”
—Blaise Pascal (1623–1662)
“What makes a regiment of soldiers a more noble object of view than the same mass of mob? Their arms, their dresses, their banners, and the art and artificial symmetry of their position and movements.”
—George Gordon Noel Byron (1788–1824)