The Lie Derivative and Interior Multiplication

Abstract

This chapter reviews two operations on differential forms, the Lie derivative and interior multiplication. These are necessary to the definition of invariant forms, horizontal forms, and basic forms in the construction of the Cartan model. The chapter then looks at the Lie derivative of a vector field and of a differential form. The Lie derivative of a differential form is defined in a similar way to the Lie derivative of a vector field, but the chapter uses the pullback instead of the pushforward to compare nearby values. One can rearrange the product formula so that it becomes the global formula for the Lie derivative. Meanwhile, the interior multiplication is also called the contraction.