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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 30,178
If the direction of the gradient of f in a point P is the direction of most/minor gradient, so a direction of the curl...
Apr10-14 09:58 AM
chogg
1 722
I'm just learning this theory and the maths is really trivial but the theory is slightly confusing me. I...
Apr9-14 08:08 PM
HallsofIvy
1 668
Hello, I'm reading the book Geometrical methods of mathematial physics by Brian Schutz. In chapter 3, on Lie...
Apr9-14 10:55 AM
George Jones
7 837
Hi, I would like to understand the left-invariant vector field of the additive group of real number. The left...
Apr8-14 03:42 AM
AlbertEi
2 659
If the gradient of f is equal to differential of f wrt s: \vec{\nabla}f=\frac{df}{d\vec{s}} so, what is the curl of f...
Apr5-14 04:33 PM
Mark44
7 825
Every conservative vector field is irrotational? Every irrotational vector field is conservative? Every solenoidal...
Apr4-14 01:55 PM
Matterwave
4 731
According to Isham (Differential Geometry for Physics) at page 115 he claims: "If X is a complete vector field then...
Apr4-14 02:50 AM
center o bass
2 666
What do you think, might be generalized the helix in the manner that I propose in the attached material?
Apr3-14 03:45 AM
micromass
5 674
As I understand it, Felix Klein sought to classify geometries with respect to what groups G that respected the...
Mar31-14 12:02 AM
homeomorphic
1 766
Let's say that ##\vec{f}## is an exact one-form, so we have that ##\vec{f}=\vec{\nabla}f##, and ##\vec{F}## is an...
Mar30-14 10:41 AM
chogg
3 744
Vector, by definition, have 2 or 3 scalar components (generally), but the curl of a vector field f(x,y) in 2D have...
Mar29-14 01:35 PM
chogg
5 896
I am reading up on principal bundles and currently I'm trying to get to grips with the definition of a connection on...
Mar28-14 01:55 PM
homeomorphic
8 963
The ##\vec{\nabla} \cdot \vec{\nabla} = \nabla^2## so, ##\vec{\nabla} \times \vec{\nabla} = \vec{0}## ? I think that...
Mar28-14 04:01 AM
arildno
6 1,015
A Lie Subgroup is defined as follows: A Lie subgroup of a Lie group G is (i) an abstract subgroup H that is (ii) an...
Mar27-14 05:17 AM
micromass
3 744
If given an one-form like: ##\omega = u dx + v dy##, dω is ##d\omega = \left ( \frac{\partial v}{\partial x} -...
Mar24-14 04:09 PM
Ben Niehoff
1 785
I found what might be the worst written book on Lie Groups. Ever. Until I find one I like better, I'm going to see if...
Mar23-14 11:17 AM
Mandelbroth
1 787
In some books, when discussing the relation between partial/directional derivatives and tangent vectors, one makes a...
Mar22-14 02:25 PM
Mandelbroth
4 894
I've been trying to prove that the closed unit ball is a manifold with boudnary, using the stereographic projection...
Mar22-14 12:25 PM
kostas230
2 675
Hello, I am looking into finding geodesic distances for an ellipsoid. I will designate two points then find the...
Mar16-14 01:00 PM
jsbxd9
0 896
Suppose we measure and plot the polarization of the Cosmic Background Radiation on a spherical plot. Could the data at...
Mar14-14 08:53 PM
Spinnor
0 688
I have a curved surface which I know the (x,y and z) coordinates for 5 separate points on it and I was wondering how...
Mar14-14 06:57 PM
Chestermiller
5 826
We call originary curve the curve for that at baseline the Frenet trihedron TNB coincides with the cartesian trihedron...
Mar11-14 04:32 AM
micromass
5 861
There are two theorems from multivariable calculus that is very important for manifold theory. The first is the...
Mar9-14 11:52 AM
micromass
1 751
Any Kähler form (?) can be written in local coordinates as \omega = \frac{i}{2} \sum h_{ij} dz^i \wedge d z^j with...
Mar8-14 08:19 AM
nonequilibrium
14 846
''..Cauchy stress tensor in every material point in the body satisfy the equilibrium equations.'' ...
Mar7-14 01:51 PM
nejibanana
1 658
I don't know very much about differential geometry but from the things I know I think that the metric is somehow the...
Mar7-14 01:29 AM
maajdl
3 619
I am struggling to make sense out some things. Hopefully someone can help or at least offer some different point of...
Mar3-14 05:42 PM
Demon117
6 1,071
I'd like to understand why i cannot seem to be able to define unit polar basis vectors. Let me explain: We have...
Mar3-14 09:44 AM
Chestermiller
1 599
Suppose that we have a Riemannian manifold (M,g) with a lower dimensional Riemannian submanifold (N,h) and a map F: M...
Mar3-14 04:17 AM
center o bass
0 538
In wolframpage there is follows definition for shape operator in a given point by vector v: ...
Mar2-14 11:25 AM
Mark44
6 951
Thank you for taking time to read my post, I hope I am putting into the correct area of the physics forum. I am...
Mar2-14 05:29 AM
pbayer123
1 630
First, I'd like that you read this littler article (http://mathworld.wolfram.com/NaturalEquation.html). The solution...
Feb28-14 10:33 PM
Chestermiller
3 644
When I derive dθ/ds I get the curvature k of a curve. But exist too the torsion τ of a curve and I think that exist...
Feb27-14 10:25 PM
Abel Cavaşi
3 697
In the wiki, there is an explanation for what is the tangential angle in cartesian and polar coordinates. However, the...
Feb27-14 06:30 AM
Chestermiller
1 593
I hope I am able to formulate this question properly as I am not extremely versed in differential geometry. I have...
Feb26-14 08:40 PM
Chestermiller
15 1,304
I noticed that in wiki there is the follows conversion: ...
Feb26-14 04:03 PM
Jhenrique
0 569
The following definitions are correct? We associate to a circular helix a complex numbers called complex...
Feb22-14 12:45 PM
Abel Cavaşi
2 669
Hellow everybody! If ##d\vec{r}## can be written in terms of curvilinear coordinates as ##d\vec{r} = h_1 dq_1...
Feb21-14 08:10 PM
joshmccraney
5 1,134
It is known that the vector in polar coordinate system can be expressed as \mathbf{r}=r\hat{r}. In this formula, we...
Feb19-14 06:01 AM
vanhees71
3 754
How would one prove Stokes' Theorem? I'm 15. I learned about Stokes' Theorem recently and I have a decent understand...
Feb19-14 12:19 AM
mathwonk
5 1,110

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