Metric Compatible, Torsion Free, Affine Connection | Tensor Intuition

Описание: Defining some terms:

Levi-Civita Connection – this form of the Christoffel symbol comes from a form of the covariant derivative known as the Levi-Civita Connection
Torsion free, metric compatible covariant derivative

Leibniz Rule – covariant derivative of a scaled vector – covariant derivative of component (scalar) and basis vector (vector)

Connection (affine connection) – the covariant derivative is sometimes called the Connection because it tells you how to connect different parts of the manifold

Torsion Free – the indices can be switched around

Metric Compatibility – the dot product of two vectors at one part of the manifold (in one tangent space) is preserved when parallel transported to another part of the manifold (another tangent space)


Lecture Notes:
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Other Resources

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Youtube Playlists on Tensors
eigenchris
Tensors for Beginners:    • Tensors for Beginners  
Tensor Calculus:    • Tensor Calculus  
Relativity:    • Relativity by eigenchris  
Andrew Dotson
New to Tensors?    • New To Tensors? Start Here  
XylyXylyX
What is a Tensor?    • What is a Tensor?  
What is General Relativity?    • What is General Relativity?  

Books
A Student’s Guide to Vectors and Tensors by Daniel A. Fleisch
https://www.amazon.com/Students-Guide...
Spacetime and Geometry: An Introduction to General Relativity by Sean M. Carroll
https://www.amazon.com/Spacetime-Geom...