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:

    “But angels come to lead frail minds to rest
    In chaste desires, on heavenly beauty bound.
    You frame my thoughts, and fashion me within;
    You stop my tongue, and teach my heart to speak;”
    —Edmund Spenser (1552?–1599)