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Questions asking for the intuition behind some definition, conjecture, proof etc. In other words, questions designed to improve or to acquire understanding on a conceptual or intuitive level, as opposed to on a technical or formal level. When asking such a question it can be helpful to include a rough description of ones understanding of the subject at hand (on a technical level).

43 votes
Accepted

Does the Pfaffian have a geometric meaning?

The thing you are missing is one further geometric property of the $(2n{-}1)$-form $\Pi$ that Chern constructs on the unit sphere bundle $\mathsf{S}(M)$ of the oriented $2n$-manifold $M$: The fact tha …
Robert Bryant's user avatar
50 votes

What is the Levi-Civita connection trying to describe?

I think that the literal answer is that the Levi-Civita connection of $g$ is trying to describe the metric $g$ and nothing else. It is the only connection-assignment that is uniquely defined by the m …
Robert Bryant's user avatar
29 votes
Accepted

How should you explain parallel transport to undergraduates?

This may not reallly be an answer that you like, but I think that, maybe you misunderstood what Ben McKay was trying to describe. Here is a more explicit, extrinsic description that may help: Suppose …
Robert Bryant's user avatar