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Differential Geometry

- Manifolds. Tensors and forms. Connections and curvature. Differential and algebraic topology
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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 26,567
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
therealdrag0
2 7,532
How can I find the radius of a circle by knowing two points and its arc length? Do I have to use a numerical method to...
Jan8-12 10:04 AM
D H
11 7,484
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
ForMyThunder
1 7,385
for those of you who've done it, how long does it take to read it? all 13 books.
Dec4-08 10:56 AM
mathwonk
6 7,331
Hello, First of all, please excuse me if I posted in the inappropriate place.. While a student few years ago, I...
Apr20-12 11:53 AM
lavinia
44 7,312
when a space (or spacetime) is said to be maximally symmetric, does this mean that it is homogeneous?
May31-09 06:57 PM
apeiron
6 7,191
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
coalquay404
3 7,122
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
hyjta
4 7,117
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
lavinia
5 7,088
Can anybody give me an explanation about non coordinate bases and its importance?
Feb2-06 07:26 AM
George Jones
17 7,067
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
attacc
18 7,045
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
HallsofIvy
4 7,034
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
mathwonk
20 6,995
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
guhan
19 6,953
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
mathwonk
42 6,876
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
Omega137
7 6,854
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
pmb_phy
3 6,842
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 6,841
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
statdad
6 6,822
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
element4
12 6,822
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
HallsofIvy
25 6,821
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
LorenzoMath
12 6,677
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
mathwonk
27 6,664
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 6,658
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
haushofer
20 6,628
Hi i'm using Kreyszig's Introductory Functional Analysis with Applications and he proves that the set of continuous...
Jun27-10 02:44 PM
Landau
7 6,606
If I have a plane with four corner 3-D (x,y,z).. et ceteraa in a coordinate system, how do I translate and rotate it...
Jul26-05 09:37 PM
laminatedevildoll
2 6,596
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
mathwonk
25 6,562
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
Cincinnatus
4 6,558
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
HallsofIvy
5 6,550
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
MathematicalPhysicist
7 6,515
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
mathwonk
1 6,506
I found it is hard for myself to follow the book on general topology by willard, since there are too many abstract...
Jan19-10 05:34 AM
bobydbcn
10 6,420
Hello to all, can somebody explain all the details of a Surface Patch? I have read some material for that but it...
Jun8-04 12:06 AM
sambo
1 6,415
If I have a (1,1) tensor, eg a Lorentz transform, how do I write its inverse? For example: x'^\mu=\Lambda^\mu_\nu...
Mar14-09 06:23 PM
cristo
5 6,375
What is a very good differential geometry introductory text? My only background is Calculus (spivak). however, I'm...
Jul25-09 08:23 AM
slider142
8 6,355
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 6,352
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
neorich
2 6,339
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
DeaconJohn
15 6,333
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
wofsy
8 6,326

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