Differentiation, Connections, and Integration

Forms prove to be a powerful tool in differential geometry and in physics. They have many wonderful properties that we shall explore further in this chapter. We know that in physics and mathematics, integration and differentiation are important, if not essential, operations that appear in almost all physical theories. In this chapter we will explore differentiation on curved manifolds and reveal several interesting properties.


Covariant Derivative Killing Vector Parallel Transport Christoffel Symbol Exterior Derivative 
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© Springer Science+Business Media, LLC 2007

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