Levi-Civita connection [SEP] named after
Levi-Civita connection. The components of this connection with respect to a system of local coordinates are called Christoffel symbols.
History.
The Levi-Civita connection is named after Tullio Levi-Civita, although originally "discovered" by Elwin Bruno Christoffel. Levi-Civita, along with Gregorio Ricci-Curbastro, used Christoffel's symbols to define the notion of parallel transport and explore the relationship of parallel transport with the curvature, thus developing the modern notion of holonomy.
The Levi-Civita notions of intrinsic derivative
Codazzi tensor
Codazzi tensors (named after Delfino Codazzi) arise very naturally in the study of Riemannian manifolds with harmonic curvature or harmonic Weyl tensor. In fact, existence of Codazzi tensors impose strict conditions on the curvature tensor of the manifold.
Definition.
Let formula_1 be a n-dimensional Riemannian manifold for formula_2, let formula_3 be a tensor, and let formula_4 be a Levi-Civita connection on the manifold. We say that the tensor formula_3 is a Codazzi tensor if 
See also.
- Weyl–