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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
1 26,439
Hello, I've been struggling with the so often spoken idea that a metric tensor gives you all necessary information...
Y 08:14 PM
6 132
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
2 255
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
5 146
If a vector field can be decomposed how a sum of a conservative + solenoidal + harmonic field......
Apr14-14 07:29 AM
2 127
What means: ? This guy, ##\vec{\nabla}_{\hat{\phi}} \hat{r}##,...
Apr13-14 04:38 AM
11 246
Hi Let's consider the three body problem. The motion of all bodies is a manifold of dim 18. But I will consider...
Apr12-14 02:35 AM
0 125
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
6 221
After read this stretch, my doubts...
Apr10-14 03:59 PM
5 391
Given a vector field f, I can compute the rotational tendency in the direction n (∇×f·n), the translational tendency...
Apr10-14 03:42 PM
1 114
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
1 193
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
1 191
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
7 355
I am making a Geometric model for VESPR theory, which states that valence electron pairs are mutually repulsive, and...
Apr8-14 02:54 PM
0 226
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
2 225
Hi, I have a faced a research problem where I would need to recover a frame field given its connection forms. More...
Apr6-14 09:16 AM
0 217
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
7 367
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...
Apr5-14 04:31 PM
0 191
Every conservative vector field is irrotational? Every irrotational vector field is conservative? Every solenoidal...
Apr4-14 01:55 PM
4 294
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
2 236
What do you think, might be generalized the helix in the manner that I propose in the attached material?
Apr3-14 03:45 AM
5 258
I apologize if this is the wrong forum but I need access to mathematicians who know what's happening with polygonal...
Apr3-14 03:35 AM
0 199
As I understand it, Felix Klein sought to classify geometries with respect to what groups G that respected the...
Mar31-14 12:02 AM
1 329
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
3 325
If a vector field ##\vec{v}## is non-divergent, so the identity is satisfied: ##\vec{\nabla}\cdot\vec{v}=0##; if is...
Mar30-14 09:15 AM
0 264
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
5 416
I am trying to understand the magnetic gradient tensor which has nine components. There are three magnetic field...
Mar29-14 03:08 AM
0 264
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
8 446
The ##\vec{\nabla} \cdot \vec{\nabla} = \nabla^2## so, ##\vec{\nabla} \times \vec{\nabla} = \vec{0}## ? I think that...
Mar28-14 04:01 AM
6 442
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
3 354
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
1 394
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
1 430
In some books, when discussing the relation between partial/directional derivatives and tangent vectors, one makes a...
Mar22-14 02:25 PM
4 563
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
2 394
Hello, I am looking into finding geodesic distances for an ellipsoid. I will designate two points then find the...
Mar16-14 01:00 PM
0 578
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
0 478
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
5 560
We call originary curve the curve for that at baseline the Frenet trihedron TNB coincides with the cartesian trihedron...
Mar11-14 04:32 AM
5 606
There are two theorems from multivariable calculus that is very important for manifold theory. The first is the...
Mar9-14 11:52 AM
1 500
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
14 629
''..Cauchy stress tensor in every material point in the body satisfy the equilibrium equations.'' ...
Mar7-14 01:51 PM
1 522

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