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Results tagged with dg.differential-geometry
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user 30679
Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
7
votes
if $S \times \Re$ is diffeomorphic to $T \times \Re$ then are S and T diffeomorphic?
No. (Whitehead manifold) $\times \mathbb{R}$ is homeomorphic to $\mathbb{R}^4$. See Rolfsen's "Knots and Links", for example. There are uncountably many other examples in a similar vein.
- 574
5
votes
How should one present curl and divergence in an undergraduate multivariable calculus class?
One way of motivating the derivative definition of curl (or rather scalar curl in 2D) is to prove a "Mean Value Theorem" for Rectangles. Suppose that $\mathbf{F} = (M, 0)$ is a vector field defined on …
- 574