List of Formulas in Riemannian Geometry - in An Inertial Frame

In An Inertial Frame

An orthonormal inertial frame is a coordinate chart such that, at the origin, one has the relations and (but these may not hold at other points in the frame). In such a frame, the expression for several operators is simpler. Note that the formulae given below are valid at the origin of the frame only.

R_{ik\ell m}=\frac{1}{2}\left( \frac{\partial^2g_{im}}{\partial x^k \partial x^\ell} + \frac{\partial^2g_{k\ell}}{\partial x^i \partial x^m} - \frac{\partial^2g_{i\ell}}{\partial x^k \partial x^m} - \frac{\partial^2g_{km}}{\partial x^i \partial x^\ell} \right)

Read more about this topic:  List Of Formulas In Riemannian Geometry

Famous quotes containing the word frame:

    “The warped, distorted frame we have put around every Negro child from birth is around every white child also. Each is on a different side of the frame but each is pinioned there. And ... what cruelly shapes and cripples the personality of one is as cruelly shaping and crippling the personality of the other.”
    —Lillian Smith (1897–1966)