In differential geometry, differential forms are totally anti-symmetric tensors and play an important role. I am led to wonder why do we not study totally symmetric tensors as much as forms. What ...
I'm studying differential geometry and am learning about differential forms. We have a very intuitive and simple way to understand 1-forms as linear maps on from the tangent space to the base field, ...
I have been given the following problem: Let $\alpha$ be a nowhere-zero 1-form. Prove that for a (p+1)-form $\beta$ $(p\geq0)$, one has $\alpha \wedge \beta = 0$ if and only if $\beta = \alpha ...
Suppose we have a Riemann surface $M$ together with a holomorphic vector bundle $E \to M$ of rank n. let $K$ denote the canonical line bundle and let $E^*$ denote the dual bundle I am trying to ...
Let $A$ be a $n \times n$ matrix of 1-forms (for example, a connection form). Note that $A \wedge A$ is not $0$, but by using the anti-symmetry of the wedge product applied to the entries of $A$ we ...