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Let $X$ be a compact, oriented, Riemannian $n$-fold. Then we have a Laplacian operator $\Delta = d d^{\ast} + d^{\ast} d$ from $\Omega^k(X)$ to itself. We have the Hodge decomposition $\Omega^k(X) = \...

I have a way to calculate the connection 1-form $\alpha$ associated to a compact simply connected parallelizable Riemannian surface $(M,g)$ (so, $M$ is topologically a disk) and a special orthonormal ...