The Hodge star operator is a central concept in differential geometry and mathematical physics, particularly in the study of manifolds and exterior calculus. It provides a way to relate different forms on a manifold and is crucial in formulating theories such as electromagnetism in a coordinate-free manner. In this introduction, we will explore the definition, properties alongside some detailed examples to illustrate its usage.
Note: At 19:58 the Levi-Civita symbol should read 𝜀^3412 = -1 and NOT 𝜀^1234.
11 сен 2024