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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 31,375
what do we mean by "Finsler geometry is just Riemannian geometry without the quadratic Restriction " . i don't...
Nov5-10 04:09 PM
2 1,032
can we define a metric on a submanifold of as follows: M is a manifold equipped with a Riemannian metric g, we denote...
Nov5-10 02:29 PM
2 1,084
This should hopefully be a quick and easy answer. I'm running through Lee's Introduction to Smooth Manifolds to...
Nov5-10 11:33 AM
9 1,491
I dont know if this is the right place to post this question so i'll also be posting it in the GR section, but anyway....
Nov5-10 10:22 AM
0 1,320
Hello I am curious about this. Uryshon' s lemma is also known as "the first non-trivial fact of point set topology",...
Nov4-10 04:36 AM
5 1,409
if we have a vector space V,can we define the tangent bundle of V rated TV?
Nov3-10 02:47 PM
2 1,056
excuse me but if someone can give me the exact definition of a sub-elliptic differential operator . thnx a lot .
Nov3-10 03:29 AM
2 814
Let's say I want to use the spherical law of cosines to determine the distance between two points. How do I calculate...
Nov2-10 09:20 AM
1 2,006
Is there any non-orientable one-dimensional manifold ? If not, how to prove it? Thanks!
Nov2-10 07:20 AM
1 2,445
hey, i'm getting really confused with something. If i have the covariant derivative of say, constant * exp(2f), is...
Nov2-10 07:19 AM
3 1,878
Hello. I was wondering if anyone here could help me understand this method I found described in the paper: "A...
Nov1-10 12:34 PM
0 1,944
Define 2-tori as {(z1,z2)| |z1|=c1,|z2|=c2} for c1 and c2 are constants, how to show that it is diffeomorphic to S^3
Oct31-10 09:09 PM
4 1,300
So I consider myself decently strong in algebra but many of the basic, important notions in algebraic geometry are not...
Oct31-10 11:39 AM
9 2,256
I've been looking at the Birkhoff-von Neumann polytope, and the book stated that the vertices are given by the...
Oct30-10 02:18 PM
6 1,110
hello! just a quick question, does the covariant derivative of the metric give zero even when the indices(one of the...
Oct30-10 12:16 PM
3 1,363
How to find the angle of diagonal of a rectangular prism? On which plane will that be measure and why is it that so?
Oct30-10 05:16 AM
0 2,265
Hi, everyone: My prof. recently made a statement to the effect that , given a handlebody decomposition of a...
Oct29-10 07:27 PM
0 684
I might have forgotten about it cause I took a similar course two years ago. So I have this assertion: Let F be a...
Oct29-10 09:33 AM
5 1,498
Hi folks, I am following this pattern: to build a 3d model of...
Oct29-10 07:59 AM
0 948
This is from O'Neil's differential geometry. I'm having trouble parsing through the problem/hint. Given any curve...
Oct29-10 01:08 AM
2 1,409
let M be a manifold and g a metric over M . is it true that every subbundle from M must have the same metric g ?
Oct28-10 03:44 AM
5 1,128
I will preface this by saying that if anyone has the following book: Euclidean Geometry and Transformations written by...
Oct27-10 02:17 AM
5 1,306
I want a projection of Earth where distances are undistorted. i.e. 10 degrees of latitude at the equator is exactly...
Oct26-10 11:06 AM
2 1,224
Hello all, Here is my question while reading a proof. For a compact set K in a separable metrizable spce ...
Oct25-10 05:02 PM
5 1,298
I'm trying to create a program which will do these calculations. I am given Latitudes, Longitudes, and ellipsoidal...
Oct24-10 12:22 PM
1 1,831
Tensor densities are normally defined in terms of coordinate transformations. Could they also be defined as functions...
Oct24-10 09:20 AM
14 2,698
Do you agree that the following identity is true: \int_S (\nabla_\mu X^\mu) \Omega = \int_{\partial S} X \invneg ...
Oct24-10 07:06 AM
8 2,301
I get in essence what the covariant derivative is, and what it does, but im having trouble with the definition, of all...
Oct24-10 02:21 AM
8 1,264
Few days back I posted a question here that dealt with inversion geometry. A point P inside a sphere can be inverted...
Oct24-10 01:23 AM
1 1,673
Theorem: If a straight line intersects one of the sides of the asymptotic triangle ABOmega but does not pass through a...
Oct23-10 09:05 AM
0 2,371
Hello, not sure if this the right place or not to post this, but I am after a definitive answer to the definition of...
Oct22-10 10:29 PM
Moss Pauly
0 695
I'd like some help understanding three things. - What is the topology of the Grassmann manifold or oriented...
Oct22-10 02:41 PM
13 2,125
Hi everyone, I've tried googling how to calculate a straight line distance on a sphere. I got no answers for it...
Oct22-10 01:37 PM
6 1,635
Hi everyone. I have been around a problem that I cannot figure out a solution (if there is one) which is related...
Oct22-10 12:16 PM
2 2,305
Is it true that for all antisymmetric tensors F^{\mu\nu} the following identity is true: \nabla_\mu \nabla_\nu...
Oct22-10 07:36 AM
4 2,127
Hi friends; can someone tell me how to prouve that the cartan tensor is defiend in SM ( the projective sphére bundle...
Oct22-10 03:25 AM
2 972
I am writing a program that uses Snell's Law for refraction of light through two interfaces and I've encountered a...
Oct21-10 10:19 PM
0 765
Can a connected space have a countable disjoint cover of closed subsets with at least two elements?
Oct21-10 04:43 PM
15 2,347
Attached are 3 of the images I created from a simple basic Moebius Band in the ChaosPro 3.3 In each one; I severed...
Oct20-10 11:08 PM
0 2,139
Here's something that's bothering me a bit. Let f : X --> Y be a continuous function, where X and Y are topological...
Oct20-10 04:43 PM
22 2,231

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