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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 31,063
Hi there: i have a question on geodesics in a Eculidean space equipped with a metric tensor \lambda(x)*I, where I...
Nov16-07 10:42 PM
6 2,559
Hi, everyone: I am asked to show that a group G acts by isometries on a space X. I am not clear about...
Nov17-07 04:31 AM
2 2,117
I have never studied topology (other than point-set topology). I am now taking a course on manifolds using Spivak...
Nov19-07 03:55 PM
10 4,451
Supposing we have as 2 vector fields: F = x^2i + 2zj +3k and G = r^2e_r + 2\cos\Theta e_{\Theta} +...
Nov20-07 11:24 AM
3 2,138
in general, what exactly does it mean for a tensor to be non-degenerate? does it mean that the vector space...
Nov21-07 12:03 PM
Chris Hillman
7 2,622
Hi: I am going over Lee's Riemm. mflds, and there is an exercise that asks: Let M<M' (< is subset) be an embedded...
Nov23-07 11:20 PM
6 3,218
A two-dimensional Rienmannian manifold has a metric given by ds^2=e^f dr^2 + r^2 dTHETA^2 where f=f(r) is a function...
Nov27-07 04:30 PM
Chris Hillman
7 3,463
So this book I have (Mathematical Methods for Physics and Engineering, Riley, Hobson, Bence) defines curvature as...
Nov30-07 09:16 AM
2 3,278
Let q and q' be sufficiently close points on C^oo manifold M. Then is it true that any C^oo curve c:-->M where...
Nov30-07 03:59 PM
Chris Hillman
6 3,630
Which grad level subjects is more related to and plays a more important role in symplectic geometry? And will also...
Nov30-07 10:12 PM
0 2,058
What kind of tangent distributions are not integrable? Is there concrete examples with two dimensional non-integrable...
Dec1-07 01:33 AM
5 2,926
what is the tensor product's physical significance? I know what it does mathematically, but what does it mean. I have...
Dec4-07 07:03 AM
17 5,785
Sorry about the horrible confusion in this post, I am befuddled and likely spouting gibberish. Consider the general...
Dec5-07 02:17 PM
George Jones
2 3,800
Hi, everyone: I was just going over some work on Hyperbolic geometry, and noticed that the geodesics in...
Dec9-07 04:23 PM
Chris Hillman
8 5,797
Hi, I have a quick question about a derivation that has annoyed me all day. I am trying to prove, from the definition...
Dec11-07 09:48 AM
3 1,774
show that ,the set { (x,|x|);x is real number } IS NOT the image of any immersion of R into R^2 .
Dec17-07 01:26 AM
0 1,658
Hi, everyone: I am trying to show this: Given C(t) a unit-speed curve, using the usual Frenet-Serre frames...
Dec17-07 07:49 PM
0 2,390
Hi all, I'm teaching myself the algebraic side of tensors and I was wondering if you would be able to clarify a few...
Dec18-07 01:24 AM
10 11,592
I'm reviewing for my final and there is a question I cant seem to solve. If anyone could help me with it I would...
Dec22-07 12:34 AM
1 1,455
Hi, I have a question about deriving tensor identities using geodesic coordinates ( coordinates in which one can put...
Dec22-07 04:41 PM
11 10,146
Okay, So I have am elementary question to ask but it is of fundamental importance to me. First things first, I have...
Dec25-07 06:35 AM
5 5,152
Hi, everyone: In an effort to show that at any point p in a Riemannian mfld. M there is an orthonormal...
Jan1-08 12:47 PM
7 2,591
Hello: I have a doubt because I don't find the general definition of the nabla operator in order to solve my...
Jan5-08 03:42 AM
2 2,161
Thanks for the help on the other questions. I am having trouble with another derivation. Unlike the others, it's...
Jan5-08 03:43 AM
1 4,627
I'm reading through Pauli's "Theory of Relativity", which has a discussion of tensors in the mathematical tools...
Jan7-08 01:39 PM
4 2,021
What Lie groups are also Riemann manifolds? thanks
Jan8-08 02:07 PM
12 3,649
Why are Lie groups also manifolds?
Jan9-08 04:20 PM
Shaun Culver
3 2,147
Are there propagating charged waves admitted in Maxwell’s equations? (I know many of you guys posting in Tensor...
Jan10-08 09:44 PM
0 1,474
Hi, Could someone tell me why the center of the structural group in a principal fiber bundle is always included in...
Jan11-08 10:20 AM
0 4,256
Given a tensor field T(x,y,z), how would I go about differentiating it wrt spacial coordinates? I would presume...
Jan12-08 05:52 PM
0 1,773
Hi everyone, Does anyone have any recommendations on good textbooks (or websites) that help translate the...
Jan13-08 11:37 AM
4 2,376
Please forgive any stupid mistakes I've made. On p.85, 4-5: If c: \rightarrow (R^n)^n is continous and each...
Jan14-08 06:22 PM
4 2,943
1.suppose that f:X->Y is continuous. if x is a limit point of the subset A of X, is it necessarily true that f(x) is a...
Jan17-08 12:32 PM
4 2,328
I was just wondering if anyone had a decent web site explaining some of the basic terminology of differential...
Jan18-08 09:36 PM
7 2,224
Hello. I'm learning tensor analysis. I have a problem. We know that ...
Jan24-08 11:39 AM
6 3,205
This is a very basic question, but one I keep getting confused on nonetheless. Can someone explain to me the...
Jan24-08 03:40 PM
5 8,561
Can anyone recommend a reference for sphere eversions--the actual math, not one of the videos online. An online...
Jan25-08 12:03 PM
0 1,615
I need to prove the following: let p be a metric on X, and f:[0,infinity)->[0,infinity) s.t: 1.f(0)=0. 2.f is...
Jan27-08 12:09 PM
4 2,183
Hi, everyone: I am trying to understand the intersection form, and I am having trouble with the notation...
Jan27-08 03:01 PM
5 2,435
Suppose we define the Lie derivative on a tensor T at a point p in a manifold by \mathcal{L}_V (T) = \lim_{\epsilon...
Jan27-08 11:27 PM
5 3,712

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