Properties
By antisymmetry of forms,
and so . This may be compared to the exterior derivative d which has the property d2 = 0. The interior product relates the exterior derivative and Lie derivative of differential forms by Cartan's identity:
This identity defines a duality between the exterior and interior derivatives. Cartan's identity is important in symplectic geometry and general relativity: see moment map.
Read more about this topic: Interior Product
Famous quotes containing the word properties:
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)