covariant derivative उदाहरण वाक्य

This is the tactic taken by the covariant derivative approach to connections : good behavior is equated with covariance.
Thus they quickly supplanted the classical notion of covariant derivative in many post-1950 treatments of the subject.
By definition, a covariant derivative of a scalar field is equal to the regular derivative of the field.
In differential geometry, the covariant derivative makes a choice for taking directional derivatives of vector fields along curves.
Thus one might want a derivative with some of the features of a functional derivative and the covariant derivative.

With the classical covariant derivatives, covariance is an " a posteriori " feature of the derivative.
Then decompose the ambient covariant derivative of ? along " X " into tangential and normal components:
where we have taken advantage of the first covariant derivative of a function being the same as its ordinary derivative.
Cartan connections induce covariant derivatives and other differential operators on certain associated bundles, hence a notion of parallel transport.
Furthermore, many of the features of the covariant derivative still remain : parallel transport, curvature, and holonomy.