One type of this operation acts on a form the same way as would the commutator of the contraction with a vector field and another type of this operation, according to Cartan's magic formula. In curved space this operation is generalized by adding a term which includes the Christoffel symbols; that t
One type of this operation acts on a form the same way as would the commutator of the contraction with a vector field and another type of this operation, according to Cartan's magic formula. In curved space this operation is generalized by adding a term which includes the Christoffel symbols; that type of this operation is used to define parallel transport. It's not a product, but a type of this operation which squares to zero and maps an n-dimensional form to an (n + 1)-dimensional form is called an (*) "exterior" one. Functions that go through the origin twice have a location where this value is zero according to Rolle's theorem. For the square root of x, this operation gives one over the two times the square root of x, and it equals zero at a function's min or max. For 10 points, name this operation which is the inverse of an "integral" according to the fundamental theorem of calculus.
One type of this operation acts on a form the same way as would the commutator of the contraction with a vector field and another type of this operation, according to Cartan's magic formula.
derivative [accept specific types like Lie, covariant, partial, exterior] 