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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 29,785
I finally finished my big summer research project. Reviewing how it went, it is clear to me that I lack an...
Jul24-14 09:14 PM
Pond Dragon
1 116
Hey guys, I'm working on a summer research project right now in diff. geo. I'm at the point where I have to define the...
Jul23-14 11:35 PM
Greg Bernhardt
1 1,114
Does anybody know nice introductory material for K3 manifold/ surface? Some very basic exposition, maybe hidden in...
Jul23-14 11:35 PM
Greg Bernhardt
1 1,230
In Nakahara's book, the interior product is defined like this : i_{x} \omega = \frac{1}{r!} \sum\limits_{s=1}^r...
Jul22-14 07:50 PM
11 1,525
I wonder if curvature necessarily means space has been removed. The typical example is forming a "curved" surface by...
Jul22-14 02:31 AM
9 337
Hi, I have real problems with the indices here, can someone give me a step by step explanation how to compute stuff...
Jul21-14 09:00 PM
4 305
I have an object (A) at some altitude above the Earth ellipsoid, and a point (B) on the surface of the Earth. ...
Jul21-14 06:56 PM
0 180
(From another site) I think the answer is no, for ##i: S \rightarrow \mathbb R^n ## the inclusion/restriction, and...
Jul18-14 05:48 PM
3 655
I'm trying to explicitly show that \varepsilon^{0 i j k} \varepsilon_{0 i j l} = - 2 \delta^k_l I sort of went...
Jul18-14 09:11 AM
2 624
Long time reader, first time poster. Originally, it was my contention that all Lie groups could be written as the...
Jul17-14 10:36 PM
Pond Dragon
1 583
I need to use a computational software to work on tensorial hermite polynomials. The operations I want to perform are...
Jul9-14 08:46 AM
3 2,193
Hello, I'm trying to get a hang of the defintion presented in Arfken - Mathematical Methods for Physicists for 3...
Jul8-14 02:46 AM
2 1,152
I am working on a paper that provides the following formula for computing radius of curvature at a point on a surface....
Jul4-14 10:39 AM
1 2,390
I'm reading about multlinear algebra and I'm stuck at differential form and outer product. The definitions involve...
Jul4-14 12:33 AM
13 2,985
Greetings, I am attempting to compute geodesic distances on manifolds where structural data have been sparsely...
Jul1-14 10:15 PM
Greg Bernhardt
1 1,543
Hi, I have an exercise whose solution seems too simple; please double-check my work: We have a product manifold...
Jul1-14 10:15 PM
Greg Bernhardt
1 1,605
Suppose we have a foliation of leaves (hypersurfaces) with codimension one of some Riemannian manifold ##M## with...
Jun27-14 07:56 AM
2 2,924
Suppose one has a foliation of a manifold ##M## with codimension one leaves that are all isometric. What is such a...
Jun27-14 06:35 AM
3 2,028
I'm looking to prove the Global Frobenius theorem, however in order to do so I need to prove the following lemma: ...
Jun26-14 10:37 PM
Greg Bernhardt
1 1,779
A scalar field can be the exact form of a vector field (potential form)? It's make sense?
Jun26-14 03:38 PM
7 1,875
Hello, I want to find out the 'average distance' between many points on a 2D plain. That is, if you were standing on...
Jun25-14 01:17 PM
9 1,688
If two orthogonal coordinate systems (xyz and x'y'z') share a common origin, and the angles between x and x', y and...
Jun25-14 11:07 AM
16 1,664
I am trying to compute the geodesic (or tangent) radius of curvature of the geodesic circle by using the below...
Jun25-14 09:33 AM
2 1,489
i really lost with this. i see two possibilities: (1) something like, \epsilon_{abc}\partial_{a}A_{b}e_{c} with...
Jun23-14 12:29 PM
4 1,587
I recently bought a copy of S. Ramanan's Global Calculus. I skimmed around a bit. Naturally, I was confused when it...
Jun20-14 11:51 AM
8 1,959
Is possible to compute indefinite integrals of functions wrt its variables, but is possible to compute indefinite...
Jun19-14 04:44 AM
12 1,817
Hello people of Physics Forums, In my research into transmission lines, I have come across the following function:...
Jun17-14 04:59 AM
3 1,609
After watch this video, I understood that for study the behavior of the...
Jun16-14 01:26 PM
7 1,793
First I want to mention that I am not super good at maths and that I wasn't even sure if this was the right sub forum...
Jun15-14 10:51 PM
Simon Bridge
1 1,482
How do I calculate the symmetry axis of a Hyperbole ? Is there a formula? If the Hyperbole is formula : ...
Jun14-14 11:26 PM
Simon Bridge
1 1,507
I'm relatively new to locally ringed spaces and sheaves. I was aware of them before, but I lacked the mathematical...
Jun14-14 05:47 PM
5 1,857
In 2 dimensions given a scalar field f(x,y) is possible to compute the line integral ##\int f ds## and area...
Jun14-14 01:33 PM
4 1,646
The quantity ##\vec{\omega} = \vec{\nabla} \times \vec{f}## is called vorticity and is the measure of the local...
Jun13-14 01:09 AM
8 1,693
Hello everyone ,i have captured car positons at differents...
Jun11-14 05:39 AM
3 1,722
Please read the attached file to answer my question. Thanks a lot.
Jun10-14 10:44 PM
1 1,723
If ##\omega## is an exact form ##( \omega = d\eta )## and ##\Omega## is the region of integration and ##\partial...
Jun10-14 09:58 PM
1 1,543
I am making a Geometric model for VESPR theory, which states that valence electron pairs are mutually repulsive, and...
Jun8-14 08:52 PM
P. Love
3 2,430
Exist circulation in a system/circuit/vector field/anything where the path of circulation is open? Is possible to...
Jun8-14 05:39 PM
5 1,744
While reading about sheaves, I came across a beautiful definition of a manifold. An ##n##-manifold is simply a locally...
Jun8-14 03:54 PM
3 1,666
Hello, I am a novice to manifolds and higher dimensions. Could you recommend a good introductory book(s) or web...
Jun7-14 12:30 AM
14 1,971

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