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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 30,418
I'm doing a reading of Carroll's General Relativity text, and I am a bit confused about one bit of tensors....
Aug21-08 11:45 AM
5 1,928
Consider f: S1 -> S1: (cos 2 pi x, sin 2 pi x) -> (cos 2 k pi x, sin 2 k pi x). How to show directly from the...
Aug21-08 09:43 AM
1 1,339
I read, again in Spivak's Calculus on Manifolds, that the integral of 1-form over a 1-cube is equivalent to a line...
Aug19-08 01:16 PM
2 1,993
Hi people, I just need to verify that I understand this correctly. For some four dimensional manifold and group...
Aug18-08 01:46 PM
0 1,473
Hi fellas I have been reading Road to Reality by Roger Penrose, but cant go beyond chapter 8. I do not understand...
Aug17-08 12:27 PM
9 1,924
Hey, I posted earlier about the tensor covariant derivative, and the help was great, that makes sense to me now. ...
Aug12-08 11:02 AM
26 8,952
Dear forum-members, Pestered by many (in my opinion, fundamental) questions and no literature at hand to answer...
Aug12-08 10:04 AM
1 2,771
Hello, I need help. The topic is a gradient in spherical coordinates. In cartesian it is clear but in spherical...
Aug9-08 05:00 PM
3 22,529
I have a few question, I hope you can help me on some of them. 1.Show that if A (subset of R^n) is a submanifold...
Aug4-08 08:20 AM
3 1,881
I am wondering whether or not anybody has any ideas of how to visualize and calculate the Frechet distance between two...
Aug2-08 02:28 PM
0 2,142
I want to use the theorem that states that if C is the set of critical points in N of a smooth function f:N->M (where...
Aug2-08 11:39 AM
1 1,860
The SO(3) group is topologically a 3-dimensional ball of radius \pi, if the opposite points on its surface are...
Aug2-08 07:28 AM
5 1,924
I'm trying to study some basic tensor analysis on my own for practical purposes, but I'm having some problems. More...
Jul29-08 11:26 AM
6 2,814
Hi, I have a problem with deriving Einstein equations : \epsilon_{IJKL}(e^{I} \wedge R^{JK} + \lambda e^{I}...
Jul27-08 09:27 AM
0 1,599
Hello everyone! I finished school 2 months ago and at the moment I'm looking forward to my study in physics :) ...
Jul26-08 03:48 PM
3 9,907
Hi everybody! I have a question concerning tensors and hope you could help me :) ...
Jul26-08 05:28 AM
11 4,069
Hey all, This question stems from Scorpan, "The Wild World of 4-Manifolds", pg 302 (and all through that...
Jul25-08 11:01 AM
0 1,512
If there is a contravariant vector v=aa+bb+cc with a reciprocal vector system where abc]v=xbc+yac+zab ...
Jul24-08 02:50 AM
1 8,724
As I understand it, for a tensor of any rank I can produce a corresponding scalar in the following way: Create an...
Jul21-08 07:39 PM
9 2,319
So I've taken two differential topology/geometry classes both from a mathematics department. I see all over this...
Jul21-08 12:04 PM
4 1,877
Can you give me the definition of exterior covariant derivative or any reference web page ? Wiki does not involve...
Jul17-08 06:20 PM
3 3,511
Hey everyone, I am integrating something (specifically 2-forms, but I think this is a general statement) over a...
Jul16-08 09:20 AM
2 1,484
show that there is no immersion of into
Jul12-08 10:07 PM
2 1,579
In Hartshorne's book definiton of a dimension is given as follows: İf X is a t.s. , dim(X) is the supremum of the...
Jul10-08 08:26 PM
14 4,809
Hey everyone, First of all this is my first post and it's in regards to something I am (supposed to be) learning...
Jul8-08 09:14 AM
4 2,334
I'm trying to understand how to find the axis of a helix but so far I seem to be hitting a blank. How for instance...
Jul6-08 04:17 PM
15 6,581
Can someone elaborate? Let I = , A = {0, 1, 1/2, 1/3, 1/4, \cdots}. Show that the homotopy extension property does...
Jul4-08 12:48 AM
1 1,786
I hope I am posting in the right section. I am having a lot of trouble understanding what exactly CW complexes look...
Jun30-08 03:25 AM
1 2,054
Hi all, I do realize that my previous thread on CW complexes was unanswered, so perhaps I am posting my questions...
Jun30-08 02:38 AM
1 3,663
Dear friends, How is the divergence in curvilinear coordinates of a second order mixed tensor defined? I mean, shall...
Jun28-08 07:05 AM
1 1,752
A vector is drawn as an arrow, a covector (one-form) as a series of parallel lines. Is there a way to pictorially...
Jun22-08 02:21 PM
14 2,992
Hi, I'm a newbie here and I would like to kindly ask for your collective wisdom on this forum. I am working on a...
Jun19-08 07:29 PM
0 2,048
if we have or can have geodesic curves minimizing the integral \sqrt (g_{ab}\dot x_a \dot x_b ) is there a theory of...
Jun19-08 09:34 AM
2 2,906
In the attached pdf file i have a few questions on manifolds, I hope you can be of aid. I need help on question...
Jun13-08 05:57 AM
1 1,529
I am interested in creating a diagrammatic notation editor. Any ideas about how I can do this? What about using Adobe...
Jun3-08 05:36 PM
5 3,140
I'm reading through Schutz's first course in relativity book and am finding question 12 on page 83 a bit problematic....
Jun3-08 05:58 AM
1 1,534
My question is about vector addition in cylindrical coordinates: Let A = 2x + y, B = x + 2y. In rectangular...
Jun2-08 05:33 PM
2 5,520
Hi, I have a computational question which concerns forms. I want to compute the variation of the electrodynamic...
May29-08 11:01 AM
4 3,305
Usually the hairy ball theorem is cited for proving that S^2 is not parallelizable. However, hairy ball theorem is too...
May28-08 12:42 PM
27 6,885
1. The problem statement, all variables and given/known data Is the gaussian curvature at a point on the surface ...
May27-08 05:14 PM
1 2,158

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