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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
micromass
1 30,972
Suppose that I have an expression of the following form: g_{ik}(x)\pi^{kp}(x') \left( \frac{\partial}{\partial...
Jun2-07 10:28 AM
shoehorn
0 1,107
Must a physical law be able to expressed by tensor equations (forms)? If there is a quantity like finite rotation,...
Jun6-07 11:13 AM
momentum_waves
24 4,457
How to prove g^{im} \nabla_{\partial_j}R_{ilkm}=\nabla_{\partial_j}R_{lk}. of cause g^{im}R_{ilkm}=R_{lk}, but I...
Jun8-07 09:43 AM
neorayner
5 4,783
Prove the theorem (Appolonius) for the triangle ABC where A, B, C are the respective points (-a,0), (a,0), (b,C) on...
Jun18-07 05:41 PM
thagamizer
2 1,869
I was wondering about this, I've never seen any general theorem. Obviously it takes more than one, but I would think...
Jun19-07 07:24 PM
LorenzoMath
12 1,920
In 3 dimension Ricci curvature determines the Riemann curvature tensor as shown in the attachment.But i couldn't prove...
Jun20-07 03:05 AM
Scientia
0 3,882
Hello, I'm doing some early work in my PhD and I'm coding a micromechanical scheme in which I have many 4th order...
Jun20-07 10:19 AM
explain
6 6,645
Do any of you have the book Tensors & Manifolds, by Robert H. Wasserman? I was looking for another good book on...
Jun20-07 10:57 PM
pmb_phy
0 1,880
I'm trying to teach myself differential geometry from the internet, and I've hit a snag in proving homeomorphisms. ...
Jun24-07 02:17 AM
cipher_42
11 3,857
Friends i need the answers of the exercises in this book . I am working on the exercises but i cant be sure if my...
Jun27-07 03:23 PM
fresnelspot
0 5,466
plz if possible send me the evaluation steps of independent components of a symmetric and antisymmetric tensor of rank...
Jun28-07 02:44 PM
robphy
1 1,306
Let G be a 3-dimensional simply-connected Lie group. Then, G is either 1.)The unit quaternions(diffeomorphic as a...
Jun30-07 04:08 AM
Reverie
3 1,275
Hey, first I want to say my English & Math aren't the best yet, so ill be glad to explain myself again if I'll need to...
Jul1-07 12:51 PM
Niv
3 1,763
I am trying to prove the following result (I am using the notation of Felsager, Geometry, Particles and Fields) ...
Jul2-07 05:36 PM
nrqed
4 3,587
I asked this question in an SR thread started by someone else but it really belongs in this forum. I received much...
Jul4-07 11:17 AM
llarsen
29 5,995
I have a question which has perplexed me for a time and thought maybe someone here would have some insight that might...
Jul6-07 08:29 AM
llarsen
0 1,670
I need to following subjects about GRASSMANN MANIFOLDS,what do I? 1)introduction(together with details) ...
Jul9-07 09:36 AM
mathwonk
5 2,930
If x,y of R^n (as a normed vector space) are non-zero, the angle between x and y, denoted <(x,y), is defined as...
Jul11-07 09:51 AM
CompuChip
1 2,258
As far as I know, the tangent space of a manifold at a point is often defined abstractly as follows. First, we define...
Jul11-07 10:43 PM
mathwonk
14 2,662
Chris Isham said (Modern Differential Geometry for Physicists) it's fairly easy to show that the pullback bundles of a...
Jul14-07 08:19 AM
kakarukeys
6 3,298
Could anybody explain why we require that in the red box and what happens after " Particularly "...
Jul22-07 02:46 PM
Mr.M
0 1,394
Why is time a scalar? Sb says time is scalar because under two different FRAMES, t and t' are the same (for...
Jul26-07 07:30 PM
uiulic
3 2,135
Hi folks I am reworking my web site to (1) so that each page will have same font, style etc of any other page and...
Jul27-07 08:24 PM
pmb_phy
15 3,627
"Introduction to vector analysis" (Harry F. Davis, 1961) page 284 says: "Tensor analysis for physicists by...
Jul31-07 05:44 PM
robphy
1 1,526
what is the sufficient condition for the kernel of an adjoint representation to be the center of the Lie group? ...
Aug1-07 07:10 AM
LorenzoMath
1 2,548
This came up in a newsgroup but there was only one person responding who would only repeat himself regardless of what...
Aug5-07 07:27 PM
robphy
25 4,167
Hey, I asked this question in another post, but I realized I may have posted it in the wrong place:...
Aug6-07 04:06 PM
ehrenfest
0 2,082
what is the physical significance of the lie derivative? What is its purpose in tensor analysis?
Aug6-07 07:50 PM
captain
2 1,541
Is it true that f is a continuous function from A \times B to C (A, B, C are topological spaces) if and only if...
Aug11-07 10:56 AM
mathwonk
8 2,242
Hi, everyone: I have been reading Boothby's intro to diff. manifolds, and in def. 4.3, talking about 1-1...
Aug12-07 11:44 AM
WWGD
0 1,665
If a tensor acts on V x V* x V, do we say that it is i. 1 time contravariant, 1 time covariant, then 1 time...
Aug14-07 11:36 AM
dextercioby
1 2,935
I have come up with an example when I trying to learn what first countability means It says(from wikipedia) In a...
Aug17-07 05:30 AM
CompuChip
11 1,837
Is a function from R^n to R^m for aritrary m a considered a 0-form on R^n, or does 0-form refers only to functions...
Aug18-07 11:19 PM
mathwonk
9 3,392
Hi, Every Thurston Geometry (X,Isom(X)) with the exception of the geometry modeled on S^2xR can be achieved as a 3D...
Aug26-07 01:39 PM
Chris Hillman
3 1,988
plz help me to solve this identity ((\phi\lambda)\chi)+((\lambda\chi)\phi)+((\chi\phi)\lambda)=0 where () =...
Aug30-07 01:14 PM
dextercioby
1 3,388
Hi, everyone. I am new here, so I hope I am follow the protocols. Please let me know otherwise. Also, I apologize...
Aug31-07 10:55 AM
Chris Hillman
3 1,920
There is one point I don't understand about G-torsor. A Lie group G acts freely and transitively on a manifold F....
Aug31-07 11:27 AM
kakarukeys
4 3,397
I'm reading about gauge theory and the text goes through some stuff about Lie groups and algebras rather quickly. I...
Sep3-07 11:24 AM
Fredrik
4 2,477
*note before reading: pretend that the superscripts are really subscripts, for some reason , Latex is making the...
Sep10-07 12:31 AM
Hurkyl
1 1,876
Hi, everyone. I am preparing for a prelim. in Diff. Geometry, and here is a question I have not been able to...
Sep11-07 03:52 PM
quidamschwarz
10 1,950

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