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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 30,944
Dear there, A plywood sheet can bend by certain degree before it breaks. Suppose f(x,y) describes the bended...
Apr9-12 02:12 PM
0 943
Dear Folks: Here is the problem: in |z|<1, we difine a distance between any two points z1 and z2 by d(z1 , z2)...
Apr9-12 12:12 PM
Fangyang Tian
0 1,039
Dear Folks: I come across the word "cusp" in two different fields and I think they are related. Could anyone...
Apr9-12 11:22 AM
1 1,103
Dear Folks: It is well known that the preimage of a regular point is a imbedding submanifold, but is it...
Apr9-12 11:10 AM
2 1,328
What's it called when a 3D shape can be made of 2D surfaces of all the same shape and dimensions? To make a cube, I...
Apr9-12 04:01 AM
Fangyang Tian
3 2,245
Hello! I've read some lie algebra in both group theory books and differential geometry books, and is confused about...
Apr8-12 11:36 PM
Fangyang Tian
10 1,933
Hi! I'm working through this script and I'm not sure if if there is a mistake at one point, or if I'm just thinking...
Apr8-12 09:57 PM
6 1,221
I came across the following statement in this often-referenced paper on Einstein-Cartan theory (3rd page, right-hand...
Apr8-12 06:02 PM
3 1,256
Hi, I have some more questions about this stuff, which, as always, confuses me. I am (extremely slowly) working...
Apr7-12 11:14 PM
2 1,529
Dear Folks: Is there any relation between Curvature Operator and Universal Eveloping Algebra, since they look...
Apr7-12 11:36 AM
Fangyang Tian
0 966
i see the definition of differential manifolds in some book for example, NAKAHARA but what is the definition of...
Apr6-12 02:05 AM
4 1,281
Problem: In circle C chords AB and XY intersect at P. Prove that the projections of P onto AX, BX, AY , BY are...
Apr5-12 10:38 PM
0 1,005
consider we have a map. what condition should have our map that it has inverse?
Apr4-12 11:39 PM
2 1,230
Hello. I have a question that has been on my mind for some time. I always see in mathematical physics books that they...
Apr4-12 11:53 AM
9 2,070
Hi! I'm trying to work through a script on Riemannian submersions but I have some problems with one proof in...
Apr3-12 07:28 PM
7 1,218
Hi, All: It's been a long time since I did this, and I have some basic doubts; please bear with me: In Lee's...
Apr2-12 06:04 PM
4 1,701
From the things I've read on manifold geometry,metric is a property of the manifold.Maybe you can call it intrinsic....
Apr2-12 05:05 PM
12 1,802
Hi, I'm looking for software that allows me to manipulate tensors as symbols themselves, i.e. not as lists of...
Apr2-12 02:37 PM
0 1,273
I am reading through Kiselev's Geometry: Book I. It is a plane geometry textbook and in the introduction it says the...
Apr2-12 12:40 PM
8 1,870
Simple question I am confused on. If I have a tensor M^{\alpha\beta\gamma} that is totally antisymmetric in its...
Apr1-12 09:41 AM
3 1,552
Hello, I am currently going over Nakahara's Geometry, Topology, and Physics and even though I have bumped into some...
Mar31-12 12:33 PM
5 1,944
I've been thinking about complex residues and how they relate to the topology of a function's Riemann's surface. My...
Mar30-12 02:16 PM
1 1,266
How many ways in the entire world are there for computing Puiseux expansions of algebraic functions? I know of three...
Mar29-12 06:29 AM
2 1,472
I want to prove the next assertion in Jeffrey M. Lee's Manifolds and differential geometry. If \mathcal{D}_1,...
Mar29-12 01:02 AM
1 1,048
Folks, I am looking at my notes. Wondering where the highlighted comes from. Prove that a finite orthogonal set is...
Mar28-12 01:28 PM
3 1,390
I need to prove that every line is contained by at least two planes using only the incidence axioms. This is what I...
Mar28-12 12:33 PM
2 1,148
I need to prove the interior of <ABC is a convex set. I know it is. I started by defining the angle as the...
Mar28-12 12:30 PM
3 1,510
If torsion = anti-symmetric part of the connection coefficients, and ...
Mar27-12 06:50 PM
8 2,493
The following is a problem that I’m sure is considered “basic” for mathematicians. I would therefore be gracious if...
Mar27-12 01:42 PM
2 1,409
The following is a distance formula for a metric/pseudometric space. Please. Can anyone give me ANY insight...
Mar26-12 07:38 PM
0 1,180
Hello, I'm looking for an appropriate rotation representation for the following situation. I have two (always...
Mar26-12 05:08 PM
0 1,106
Hi all, I've been fiddling around with this problem for a while. I intuitively understand that the parallel...
Mar26-12 03:39 PM
1 1,262
Does anyone know if there is a non-Euclidean geometry(or something like that) where the circle becomes a line or a...
Mar25-12 05:44 PM
9 2,182
Hello everyone! Could someone tell me how to evaluate the integral \int_{B_{\delta}(p_0)}{\frac{1}{(1 + d^2(p_0,...
Mar25-12 04:12 PM
0 963
Hi guys, I have questions about algebraic functions and not sure where to ask. Hope it's ok here. Given the...
Mar25-12 03:35 AM
4 1,342
(X,\rho) is a pseudometric space Define: x~y if and only if ρ(x,y)=0 (It is shown that x~y is an equivalence...
Mar25-12 03:13 AM
2 1,471
Hello all I was hoping someone could help me with the following problem. I work on the railroads and my task is...
Mar24-12 12:28 AM
1 1,656
Ok, so I don't have much of an intuition for frame bundles, so I have some basic questions. A frame bundle over a...
Mar23-12 07:41 PM
39 3,999
How do I show that Maslov index satisfies the next property (product property). Let \Lambda : \mathbb{R} /...
Mar23-12 09:56 AM
2 1,167
Given the complete classification of finite simple groups, can one say that the number of all conceivable 2D/3D...
Mar23-12 06:21 AM
M Quack
3 1,148

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