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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 31,152
Left invariant fields on a group G satisfies a lie algebra; say we have an n-dimensional Lie algebra for which the...
May15-14 08:35 AM
center o bass
7 1,335
If a vector field ##\vec{v}## is non-divergent, so the identity is satisfied: ##\vec{\nabla}\cdot\vec{v}=0##; if is...
May14-14 03:48 PM
3 1,054
I am not able to solve the following problem #1) Prove that the normal to parabola y2=4ax at (am2,-2am) intersects...
May14-14 04:11 AM
Simon Bridge
3 498
Vector fields generate flows, i.e. one-parameter groups of diffeomorphisms, which are profusely used in physics from...
May12-14 11:15 PM
33 1,647
I've been thinking about this quite a bit. So it is clear that one can determine the Christoffel symbols from the...
May7-14 04:16 PM
5 757
I am trying to understand the magnetic gradient tensor which has nine components. There are three magnetic field...
May6-14 01:04 PM
3 1,071
Given a curve ##\gamma: I \to M## where ##I\subset \mathbb{R}## and ##M## is a manifold, the tangent vector to the...
May6-14 12:39 PM
1 583
Suppose we have a vector field ##V## defined everywhere on a manifold ##M##. Consider now point ##p \in M##. As a...
May5-14 04:27 PM
center o bass
8 780
I apologize if this is the wrong forum but I need access to mathematicians who know what's happening with polygonal...
May4-14 10:19 PM
Greg Bernhardt
1 851
Hi all, I have a few questions on the two spaces S^1/Z_2 and T^2/Z_2. Am I correct in saying that the first space...
May4-14 10:19 PM
Greg Bernhardt
1 843
Hi, I have a faced a research problem where I would need to recover a frame field given its connection forms. More...
May4-14 10:19 PM
Greg Bernhardt
1 833
Hi Let's consider the three body problem. The motion of all bodies is a manifold of dim 18. But I will consider...
May4-14 10:19 PM
Greg Bernhardt
1 805
Now this is a bit of a mix of a math and a physics question, but I think it is best asked here. Assume we are...
May4-14 04:13 PM
7 971
I have: dVμ = (∂Vμ/∂xη)dxη where Vμ is a contravariant vector field I believe the () term on the RHS is a...
May1-14 07:37 PM
2 623
Hello, I am having a problem about the nature of the measurements of the intervals ds's forming out of...
Apr29-14 04:24 PM
2 752
For someone who does not already know Lie group and bundle theory, the formulation of covariant derivatives through...
Apr28-14 09:51 PM
1 747
Hello, i don't know if my question is well posed, if i have a symmetric tensor Sij = (∂ixj + ∂jxi) / 2 with xi...
Apr21-14 07:23 PM
1 857
Hello, I've been struggling with the so often spoken idea that a metric tensor gives you all necessary information...
Apr16-14 08:55 AM
7 1,027
My knowledge on this topic is a bit sketchy. I realize that there is a whole branch of math out there devoted to...
Apr14-14 07:46 PM
2 951
When I take the differential of y wrt t (being t a parameter (time)) I get the velocity of the y-coordinate, if take...
Apr14-14 08:02 AM
5 816
If a vector field can be decomposed how a sum of a conservative + solenoidal + harmonic field......
Apr14-14 07:29 AM
2 760
What means: ? This guy, ##\vec{\nabla}_{\hat{\phi}} \hat{r}##,...
Apr13-14 04:38 AM
11 931
1st which is the math definition for circulation (##\Gamma = \int_s \vec{f}\cdot d\vec{s}##)? And 2nd, what means...
Apr11-14 08:51 AM
6 1,017
After read this stretch, my doubts...
Apr10-14 03:59 PM
5 1,026
Given a vector field f, I can compute the rotational tendency in the direction n (∇fn), the translational tendency...
Apr10-14 03:42 PM
1 654
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
1 751
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
1 693
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
7 890
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
2 688
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
7 859
Every conservative vector field is irrotational? Every irrotational vector field is conservative? Every solenoidal...
Apr4-14 01:55 PM
4 758
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
2 695
What do you think, might be generalized the helix in the manner that I propose in the attached material?
Apr3-14 03:45 AM
5 704
As I understand it, Felix Klein sought to classify geometries with respect to what groups G that respected the...
Mar31-14 12:02 AM
1 810
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
3 775
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
5 951
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
8 1,020
The ##\vec{\nabla} \cdot \vec{\nabla} = \nabla^2## so, ##\vec{\nabla} \times \vec{\nabla} = \vec{0}## ? I think that...
Mar28-14 04:01 AM
6 1,099
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
3 776
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
1 825

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