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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 31,356
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
0 1,113
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
24 4,491
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
5 4,816
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
2 1,879
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
12 1,963
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
0 3,909
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
6 6,711
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
0 1,897
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
11 3,883
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
0 5,498
plz if possible send me the evaluation steps of independent components of a symmetric and antisymmetric tensor of rank...
Jun28-07 02:44 PM
1 1,310
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
3 1,288
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
3 1,773
I am trying to prove the following result (I am using the notation of Felsager, Geometry, Particles and Fields) ...
Jul2-07 05:36 PM
4 3,611
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
29 6,037
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
0 1,685
I need to following subjects about GRASSMANN MANIFOLDS,what do I? 1)introduction(together with details) ...
Jul9-07 09:36 AM
5 2,949
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
1 2,278
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
14 2,682
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
6 3,353
Could anybody explain why we require that in the red box and what happens after " Particularly "...
Jul22-07 02:46 PM
0 1,404
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
3 2,151
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
15 3,686
"Introduction to vector analysis" (Harry F. Davis, 1961) page 284 says: "Tensor analysis for physicists by...
Jul31-07 05:44 PM
1 1,532
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
1 2,569
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
25 4,208
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
0 2,090
what is the physical significance of the lie derivative? What is its purpose in tensor analysis?
Aug6-07 07:50 PM
2 1,547
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
8 2,256
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
0 1,678
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
1 2,954
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
11 1,851
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
9 3,425
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 1,997
plz help me to solve this identity ((\phi\lambda)\chi)+((\lambda\chi)\phi)+((\chi\phi)\lambda)=0 where () =...
Aug30-07 01:14 PM
1 3,412
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 1,931
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
4 3,408
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
4 2,492
*note before reading: pretend that the superscripts are really subscripts, for some reason , Latex is making the...
Sep10-07 12:31 AM
1 1,888
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
10 1,965

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