Differential geometry is the application of differential calculus in the setting of smooth manifolds (curves, surfaces and higher dimensional examples). Modern differential geometry focuses "geometric structures" on such manifolds, such as bundles and connections; for questions not concerning such ...

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Symmetric and wedge product in algebra and differential geometry

I have been struggling with this issue for a while (and asked a similar question here), but still not found a satisfying answer. The question boils down to: which is the correct identity? $dx \, dy ...
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Alexandrov embedness and branch points

Let assume that $\Sigma_n$ is a sequence of compact surfaces in $\mathbb{R}^3$ of fixed genus. We assume that the surfaces are Alexandrov embedded, that is to say there exits an immersion $i_n$ from ...