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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 31,142
Can someone explain the concept of Quotient topology. I tried to read it from a book on topology by author "James...
Nov28-10 05:59 AM
6 8,015
Wiki says it's 1 0 0 sin^2\theta My book says it's cos˛\theta 0 0 1
Jul20-06 09:34 AM
3 7,929
Can someone please explain to me what is the tensor product and any good elementary tensor algerbra books?
Nov13-08 09:41 AM
14 7,863
Having some knowledge of differential geometry, I want to self-study topology. Which of the two areas shall I study...
Apr30-10 10:47 AM
5 7,835
Can we curl a stress tensor? What physically meaning will it be?
May17-07 08:02 PM
Chris Hillman
7 7,755
I'm doing some programing and I am wondering how I can find the length of a Polygon's side (variable number of sides)...
Sep15-08 03:36 PM
2 7,716
U = e^{\frac{1}{2} B} = \cos(\frac{1}{2} \theta) + b \sin(\frac{1}{2} \theta) we can then write: U = e^{\frac{1}{2}...
Feb6-07 06:39 PM
43 7,695
Could anybody please give advice for the study of complex analysis, Riemann surfaces & complex mappings. These...
Feb4-08 08:56 PM
3 7,686
When we seek the extreaml value of the functional \Phi(\gamma) = \int_{t_0}^{t_1} L(x(t),\dot{x}(t),t)dt where x can...
Dec31-06 04:03 AM
3 7,684
when a space (or spacetime) is said to be maximally symmetric, does this mean that it is homogeneous?
May31-09 06:57 PM
6 7,575
I was reading lethe's thread on differential forms and suddenly it dawned on me that I had no idea what differential...
Aug10-04 07:07 PM
20 7,552
i am a student of physics i do not know much about the chern number i wonder why the chern number must be an...
Jul7-11 11:24 AM
12 7,511
Hi, I don't know if this is the right place to post, but can someone help me understand what differential forms are...
May15-09 01:33 PM
19 7,503
Being not an expert, my question might sound naive to students of mahematics. My question is how on earth a Lie group...
Jun16-13 02:32 AM
20 7,436
Can anybody give me an explanation about non coordinate bases and its importance?
Feb2-06 07:26 AM
George Jones
17 7,390
Although, the dot product works in infitine dimensions, it is not the case for the cross product. Anybody know in what...
Mar6-05 04:22 PM
4 7,373
Hi, I have met a problem, that is how to prove transformation law for Christoffel symbol of first kind. I have read...
May24-09 03:54 AM
4 7,359
If a vector is simply "any quantity having magnitude and direction", then how can a vector's components NOT transform...
Apr20-07 11:53 PM
42 7,348
i've been trying to find a good set of lecture notes for independent study on the subject. I wen to the one in the...
Jul23-06 12:48 PM
18 7,318
I need to show that a countable intersection of open and dense sets (the sets are open and dense at the same time) in...
Sep26-08 03:17 AM
7 7,294
How do you prove that for a set of coordinates you are supposed to take \mathrm{d}s^2=\mathrm{d}x_i\mathrm{d}x^i for...
Jan31-10 08:26 AM
25 7,284
Hi can someone help me prove this identity? I'm having trouble understand the role of the interior product or more...
Dec23-06 07:14 AM
3 7,283
hi i want to know why while dealing with any noise based application noise is assumed to be gaussian distributed? ...
Oct23-08 02:58 PM
6 7,260
Ruslan Sharipov has a nifty online textbook on this subject. It's written in interactive do-it-yourself style. Give it...
Mar24-04 03:57 PM
3 7,196
Just wondering if Traces can be applied to tensors. If the Ricci tensor is Rii then is sums over diagonal elements....
Jan11-10 12:02 PM
7 7,129
there is a general result that RPn is orientable if n is odd while non-orientable if n is even how to prove this...
Sep20-10 02:24 PM
25 7,128
Hi I'm looking for a simple definition fo the affine connection because I can't understand it's meanning , that...
Apr9-08 01:55 PM
12 7,055
Hi everybody, How can one show that the tangent bundle TS˛ of the 2-sphere is not trivial ? I know we can use the...
Mar3-09 08:32 AM
8 7,039
What is a very good differential geometry introductory text? My only background is Calculus (spivak). however, I'm...
Jul25-09 08:23 AM
8 6,973
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 6,958
Hi , everyone I have a problem with geodesic equation . I know the method of solving it , but I can't understand the...
Apr15-08 05:21 PM
the shadow
14 6,940
Can somone remind me how to see that the Lie derivative of a vector field, defined as (L_XY)_p=\lim_{t\rightarrow...
Oct18-09 01:38 PM
20 6,938
I started to reread Spivak's A Comprehensive Introduction to Differential Geometry last night, for the sake of...
Sep29-13 09:01 AM
5 6,917
I hope I am posting in the right section. Up to today I was assuming that earth is a sphere, and I was using the...
Nov23-10 02:45 AM
5 6,899
Hi i'm using Kreyszig's Introductory Functional Analysis with Applications and he proves that the set of continuous...
Jun27-10 02:44 PM
7 6,852
If I have z=f(x,y), then how would I go about finding the inverse function? More specifically, say I have a...
May11-06 04:57 PM
1 6,850
Dear All, I have inherited a few rotation matrices through some old computer code I am updating. The code is used...
Dec3-10 03:14 PM
2 6,848
Definition of surface from Pressley's "Elementary differential geometry": A subset S of \mathbb{R}^3 is a surface...
Oct27-06 12:31 PM
matt grime
9 6,807
edit: This thread might need moved, sorry about that. Hi, I have ended up on this site a few times after searching...
Dec15-09 05:56 AM
5 6,789
I need to show a particular map f:M-->N is an isometry (globally). M,N are riemannian manifolds, p is a point on M....
Mar16-08 10:34 PM
4 6,781

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