All Questions

Fix a compact Riemannian manifold $M$ (leaving the metric implicit). What I'd like to know is if the corresponding Hodge decomposition of smooth $n$-forms $$ \Omega^n(M) \simeq \mathcal{H}^n(M)\oplus ...

Let $\omega,\eta$ be two 1-forms on a manifold $M$. I'm interested in an expression for $$ \delta(\omega\wedge\eta) $$ where $\delta$ is the co-differential operator $\Lambda^2(M)\to\Lambda^1(M)$. ...

Let $f,g:\mathbb{R}^m \to \mathbb{R}^n$ be two smooth functions and let $k$ be a strictly positive integer. Write $f \sim_k g$ if at each point in the domain, the determinants of all $k \times k$ ...