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 Yearling
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Aug
18
comment Prerequisites for differential topology
It's actually somewhat of a misconception among beginning students that one needs a solid knowledge of point-set topology to study differential topology (perhaps since the name contains "topology"), but really diff top is the study of smooth manifolds, and to study those one doesn't need most of the machinery of general topology (due to the "nice" nature of smooth manifolds). The topology one develops in a course on analysis is probably enough. Munkres "Analysis on manifolds" covers most of the topics you mention.
Aug
18
answered Rigorous meaning of the expression $dz = dx + idy$
Aug
12
comment Help with an infinite sum of exponential terms?
There is indeed no closed form expression for this series. But one can approximate it's value as a Gaussian integral by the Euler-Maclaurin formula: en.wikipedia.org/wiki/Euler%E2%80%93Maclaurin_formula
Aug
9
comment Error when computing geodesics in hyperbolic half plane
Sorry, I had made a careless error in deriving the differential equation. The correct form allows us to write an explicit solution. I've fixed this in the latest version.
Aug
9
revised Error when computing geodesics in hyperbolic half plane
Error
Aug
9
answered Error when computing geodesics in hyperbolic half plane
Aug
9
comment Error when computing geodesics in hyperbolic half plane
Ignore my comment. You are right in that an appropriate semicircle, regardless of the center should satisfy the equation. Answer upcoming in a bit.
Aug
9
comment Error when computing geodesics in hyperbolic half plane
There's no reason that the semi-circle should be centered at $0$ which is what you're assuming when using your parametrization.
Aug
8
comment I am confused by the different definitions of manifolds.
The definition of a smooth manifold shouldn't be complicated since it's a fairly intuitive object. Practically speaking if you wanna see whether a topological space is a manifold or not, you first find a suitable open covering, map each set in the open covering homeomorphically into R^n and check whether the "transition functions" on the areas of overlap are smooth.
Jul
2
comment Calculating euler number of disk
As for the equivalence of the two formulas describing the geodesic curvature, I'd have to think about it since I've only explicitly worked with the classical one I wrote above. It is written out in terms of Christoffel symbols here: mathworld.wolfram.com/GeodesicCurvature.html
Jul
2
answered Calculating euler number of disk
Apr
2
comment Kähler–Einstein condition
It's quite apparent from how these objects are defined. Two two-forms are proportional if and only if the functions in front of the $dz^i \wedge d\bar{z}^{\bar{j}}$ are proportional, which follows from the fact that they are a basis for the space of (1,1) forms.
Apr
2
answered Kähler–Einstein condition
Feb
1
awarded  Yearling
Jan
1
answered Symmetric matrices and exponentials
Sep
8
answered differential equation, chain rule problem
Aug
17
answered Equations of a projective variety from parametric ones
Jul
31
answered Do two points determine a unique line in 4D space?
Jun
8
awarded  Tumbleweed
Jun
1
asked Function fields for genus 2 curves