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Differential Geometry

- Manifolds. Tensors and forms. Connections and curvature. Differential and algebraic topology
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Jan16-12 Greg Bernhardt
Please post any and all homework or other textbook-style problems in one of the Homework & Coursework Questions...
Feb23-13 09:25 AM
1 30,955
Can someone please explain this to me. Let X = fundamental group of a genus 2 surface Let Y = fundamental group of...
Nov14-09 06:49 PM
1 1,668
Hey, Could anyone help some up briefly what it means if the fundemental group of a space X is trivial. As i...
Nov14-09 09:34 AM
1 1,243
I'm trying to find the equation of a curve in R3 where k=t=a/(s^2+b) where k is the curvature, t is the torsion and...
Aug24-09 09:26 PM
1 2,863
I have this question from Nigel Hitchin's notes in PG: "Let V be 3-dimensional vector space with basis v1,v2,v3 and...
Sep4-09 03:42 AM
1 1,396
How difficult is Spanier's Algebraic Topology text to understand? How about the exercises?
Aug24-09 05:43 PM
1 3,078 also see...
Aug24-09 07:45 PM
1 1,542
how is discrete metric space given by d((x1,x2,....xn)(y1,y2,....yn))=0 if xi=yi else 1 ...
Aug24-09 08:03 AM
1 1,453
I'm trying do derive the vorticity equation \begin{align}\frac{D\vec\omega}{Dt} &= \frac{\partial \vec...
Aug25-09 10:10 PM
John Creighto
1 1,351
So, in my studies of math so far, we can take a certain geometry (or just any function) and analyze it, and ask...
Aug29-09 04:07 PM
1 1,009
I am simply trying to understand why dS space has a signature (4+1) ? Good old familiar Minkowski space is of course,...
Sep1-09 07:53 AM
George Jones
1 1,073
Hello, for a game with friends I'm trying to determine a plausible geographical centre of a small country where I...
Sep4-09 03:04 PM
jim mcnamara
1 1,111
if a set A is both open and closed then it is R(set of real numbers) how we may show it in a proper way
Sep10-09 02:36 PM
1 999
Hi there, Is there an "easy" way to find a tangent space at a specific point to an implicitly defined manifold? I...
Sep28-09 12:56 PM
1 1,374
D={z in C | |z|<1} e: DxD -> R by e(z,w)=|(z-w)/(1-w'z)| (here the w'=the conjugate of w, not sure how to insert a...
Oct3-09 03:44 PM
1 2,802
P.S. This was supposed to go into the homework forum. I had windows open for both forums and I ended up using the...
Oct6-09 02:05 PM
1 3,312
What is the orientation of the largest equilateral triangle contained within a square?
Oct7-09 01:45 AM
1 1,169
What would be the euler angles of rotation 2pi/3 about the line x=y=z? If something were in the xy plane and it...
Jan1-10 04:49 PM
1 2,695
I've read somewhere a proof of Gromov's nonsqueezing theorem using the fact that the action is a symplectic invariant...
Oct10-09 03:31 PM
1 1,170
I am not sure how to prove there is no Lebesgue number for an open cover {(1/n,1)} of interval (0,1). If I take any...
Oct13-09 03:03 PM
1 2,439
Hi how to find 3D point(lie on line) on the 3D line with given distance and from given 3D point(this is also lie...
Oct14-09 12:35 AM
1 3,350
Afternoon, I'm studying Engineering Dynamics (4th Year Undergraduate) and I was wondering if anyone can point me to...
Oct16-09 10:44 AM
1 1,093
Hey guys, anyone know what the LaTeX code for the "cut" is? I've tried /lrcorner but that doesn't seem to be the right...
Oct19-09 06:09 PM
1 1,375
I am looking for some worked examples of calculating moment maps. I have to calculate some moment maps but have no...
Nov1-09 01:24 AM
1 1,561
One of the exercises in the text I'm using for self-study asks to prove that the union of a pair of atlases A and B on...
Oct30-09 06:58 PM
1 944
Dear all, Studying for prelims, I would like to know the following. I attached the question as well(sorry). Why do...
Nov14-09 06:56 PM
1 1,290
Here is a similar one that again tells me that my undestanding of the notions is still not there. I would like to know...
Nov11-09 07:35 PM
1 1,269
The Apollonian Packing is generated by starting out with 3 mutually tangent circle and then using descartes theorem to...
Dec26-09 03:14 PM
1 2,446
how do I show a topological space X with an order topology is regular. Ive shown it is hausdorff already.
Nov23-09 05:44 PM
1 1,361
So I'm trying to understand the statement: On a complex manifold with a hermitian metric the Levi-Civita connection on...
Dec5-09 03:54 PM
1 2,261
Let \theta be the angle between the diagonal of the unit cube in R^{n} and one of its axes. Find lim \theta (n)...
Dec14-09 05:55 AM
1 1,273
In calculus, the definition of the arc length of some curve C is the limit of the sum of the lengths of finitely many...
Dec22-09 07:23 AM
1 1,810
Let F = \left\{f : Is F complete , under the given norm ? My approach was to look at the pointwise limit of an...
Dec24-09 11:42 PM
1 2,747
Why all two dimensional manifolds are conformally flat? Why all manifolds with constant sectional curvature are...
Jan6-10 05:17 AM
1 1,741
What can we tell about Lie group if we know its Lie algebra. Let's consider the following example: we have three...
Jan10-10 06:41 AM
1 1,240
Hi, I was given the following problem, and i couldn't solve it yet: Give a bijection between the elements of...
Jan12-10 09:23 AM
1 1,383
Hello everyone, While studying properties of Riemann and tensor and Killing vectors, I found this notation/concept...
Jan14-10 05:47 PM
Ben Niehoff
1 1,333
Is there any difference to the meaning of these terms? I'm keep running across both of them.
Jan16-10 02:39 AM
1 1,147
What is a question in topology asking of me when it says show that the topology of S1 and a quotient space agree?
Jan20-10 09:14 AM
1 1,019
I'm self studying topology and so I don't have much direction, however I found this wonderful little pdf called...
Jan20-10 09:27 PM
1 3,365
I am aware that a vector is a first-order tensor, and that a second-order tensor has nine components in three-space,...
Jan23-10 04:42 PM
1 1,222

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