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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 30,166
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 1,664
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 1,237
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 2,667
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 1,085
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 1,367
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 1,546
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
1 940
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 1,280
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 1,250
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 2,431
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 1,335
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 2,248
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 1,263
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 1,804
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 2,735
Why all two dimensional manifolds are conformally flat? Why all manifolds with constant sectional curvature are...
Jan6-10 05:17 AM
1 1,726
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 1,230
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 1,360
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 1,323
Is there any difference to the meaning of these terms? I'm keep running across both of them.
Jan16-10 02:39 AM
1 1,139
I'm kind of shaky on a lot of high school Geometry that is going more or less unused in my Physics and Calculus...
Jan24-10 03:19 PM
1 4,294
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 1,014
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 3,321
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 1,213
Hello, I have encountered an exercise in my differential geometry book: to derive the parametrisation and the...
Jan24-10 03:56 PM
1 2,199
I have a sphere with the equation (x-3)2+(y-2)2+(z+5)2=36 two question: 1. how do I find the equation of the...
Jan25-10 07:50 AM
1 5,245
I'm studying for an exam which is a couple months away and I found an old exam which asks the following: Find the...
Jan30-10 02:13 AM
1 1,179
heeello friends!;] i have book "wstęp do wspˇłczesnej geometrii rˇżniczkowej" written by Konstanty Radziszewski, this...
Feb2-10 08:28 PM
1 1,500
Hello, I posted a similar question long time ago, but after working on it I am still unable to arrive at a solution....
Feb4-10 11:53 AM
1 1,584
Hello:) let make a metric tensor, let it make simple, for random 2-dimentional curved space, ex....
Feb4-10 06:39 AM
1 1,311
I'm trying out some exercises in differential geoemtry and came accross this one: If \gamma(t) is unit-speed, and...
Feb6-10 09:48 PM
1 1,149
If you specify all 6 distances between 4 points A, B, C, D you fix a tetraeder. If you now give three distances AM,...
Feb7-10 05:45 PM
1 979
The Gauss curvature of a surface in R^3 is intrinsic i.e. it is an invariant of local isometry. For a hyper-surface...
Feb8-10 09:25 PM
Ben Niehoff
1 1,489
In John Lee's books "Introduction to smooth manifolds" and "Riemannian manifolds", a tensor of type \begin{pmatrix}k\\...
Feb18-10 11:24 PM
1 1,335
Hi Guy's I was wondering If anyone new of a good link about the P-adic metric Strong triangle inequality. I am trying...
Feb17-10 04:56 AM
1 3,458
I'm working thru Thirring's Classical Mathematical Physics. The lie derivative is defined and used on a vector field....
Feb13-10 01:57 AM
Ben Niehoff
1 1,044
Under what conditions can the metric tensor be integrated to a global metric function? i.e., a function g(x,y) that...
Feb13-10 11:31 PM
1 1,116
Suppose you're given a 4 tuple and told that its scalar product with any 4-vector is a lorentz scalar. How do I show...
Feb18-10 12:36 PM
1 1,111
when I first learned about homeomorphic sets, I was given the example of a doughnut and a coffee cup as being...
Feb17-10 09:53 PM
Ben Niehoff
1 2,546
For my tensor analysis class we have to do some project/research on tensor applications. I've done a search and I...
Feb18-10 10:56 PM
1 1,521

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