Math - Ricci Tensor

This page describes the Ricci Curvature Tensor in Cartesian and Spherical coordinate systems. 

Motivation for derivation of Ricci Tensor from Riemann Tensor

In General - Ricci Curvature Tensor From Reimann Curvature Tensor

Ricci Curvature Tensor for 3-Space

Ricci Curvature Tensor for Space Time 

Ricci Tensor using Index Notation 

Ricci Tensor for Space-Time using Cartesian Coordinates -  ( t, x, y, z )

Ricci Tensor for Space-Time using Spherical Coordinates -  ( t, r, theta, psi)

Ricci Tensor - Summation of Sectional Curvatures - Space-Time for Spherical Coordinates 

Each of the 16 components in the Ricci Curvature Tensor is composed of 40 terms of Christoffel Symbols.  

Each of the components of the Ricci Curvature Tensor written out.