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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
micromass
1 26,498
I need to show that if X is Lindelof and Y is compact then XxY is Lindelof. Now let ,XxY=U(A_\alpha x B_\beta) for...
Apr22-08 01:47 PM
MathematicalPhysicist
0 2,251
Hi there, I'm reading over my Lie groups notes and in them, in the introductory section on manifolds, I've written...
Apr22-08 02:53 AM
mrandersdk
22 3,933
Im reviewing material for the exam and came across this question: Let pi_1:RxR->R be the projection on the first...
Apr20-08 05:46 PM
WWGD
3 3,138
Could any one help me to prove the following question: "How can we show that the set {A in GL(n;R) | det(A)>0} is...
Apr20-08 05:24 PM
WWGD
4 2,382
Could someone please help me with: if N,M are diffeomorphic manifolds, what property do they share that...
Apr15-08 08:07 PM
wofsy
22 4,278
Hi , everyone I have a problem with geodesic equation . I know the method of solving it , but I can't understand the...
Apr15-08 05:21 PM
the shadow
14 6,837
I'm a bit confused as to how the text Tensor Analysis on Manifolds, by Bishop and Goldberg on page 6. The authors...
Apr14-08 04:54 PM
Doodle Bob
3 1,994
Does any one know why a max abliean subgroup of a compact Lie group is not necessary Max. torus? any exmaple? Thanks!
Apr12-08 01:00 PM
jojoo
0 2,000
Hi guys I was first introduced to diagrammatic notation in Roger Penrose's book "Road to Reality". I wanted to...
Apr10-08 06:40 PM
shoehorn
1 1,804
I am trying to understand differentiable manifolds and have some questions about this topic: We can think of a...
Apr10-08 07:14 AM
wofsy
3 2,214
Another question: How do we define compatibility of atlases and a maximal atlas? why do we need to define them?...
Apr9-08 08:03 PM
wofsy
15 3,263
noob here * indicates multiply (or 'operate on'), d_c is partial derivative w.r.t. c tensor indices have always...
Apr9-08 04:20 PM
jiggers
0 2,255
Hi I'm looking for a simple definition fo the affine connection because I can't understand it's meanning , that...
Apr9-08 01:55 PM
LorenzoMath
12 6,671
Affine spaces can be regarded as smooth manifolds if we take the natural topology and affine coordinate charts as...
Apr9-08 07:51 AM
wofsy
9 2,947
Hi everyone, I've been studying on Gauss map for while. I have a question about the isotropy subgroup. I know its...
Apr9-08 07:03 AM
saddy
0 1,418
Hi everyone, I've been studying on Gauss map for while. I have a question about the isotropy subgroup. I know its...
Apr9-08 06:41 AM
saddy
0 2,042
I have a quetion about the forms. When we say, "differential forms of degree one (or more)" rather than degree...
Apr9-08 06:26 AM
Doodle Bob
8 2,244
My assignment is to prove that the next groups: SO(n),U(n),SL(n,R) are path connected, and that the groups...
Apr8-08 09:51 PM
wofsy
10 4,701
Hello. Suppose that \sigma: (M, g) \to (N, h) is an isometric diffeomorphism between two Riemannian manifolds M and...
Apr8-08 09:19 PM
wofsy
4 1,697
The product of the principal curvatures of a surface in Euclidean 3 space, though defined extrinsically, is actually...
Apr8-08 08:44 PM
wofsy
5 1,718
My professor recently defined immersions and embeddings in class, but he didn't really make any attempt to motivate...
Apr8-08 03:10 PM
wofsy
8 2,785
In calculus on manifolds, within one of the problems of this book the dual space is indirectly defined. I'll quote: ...
Apr8-08 08:12 AM
wofsy
9 2,554
I'm taking a class in differential geometry in the fall and I wanted to be sure to be well prepared. Are there any...
Apr7-08 09:52 PM
hanskuo
22 3,431
Is it possible to have a tangent vector field on the unit 2-sphere x^2+y^2+z^2 =1 in 3D which vanishes at exactly one...
Apr7-08 09:19 PM
wofsy
6 5,077
A hypersurface of Euclidean space inherits a Riemannian connection by tangential projection of the flat Euclidean...
Apr7-08 07:29 PM
wofsy
0 1,061
Does anyone know what the Dirac delta function would look like in a space with curvature and torsion? The Dirac delta...
Apr7-08 12:03 PM
friend
6 2,795
Hello all. In a quite easy to follow short piece by Edmond Bertschinger entitled Introductio to Tensor Calculus for...
Mar27-08 06:40 PM
matheinste
4 9,997
Hi, everyone: I apologize if this is out of place. Please let me know if so, and feel free to remove. I am...
Mar27-08 02:27 PM
WWGD
10 2,109
My differential forms book (Flanders/Dover) defines an inner product on wedge products for vectors that have a defined...
Mar27-08 11:13 AM
Peeter
6 4,673
Hello, One says that an odd derivation d is a differential modulo another differential d' if this two things hold:...
Mar23-08 12:34 AM
astros
2 1,494
This semester i'm taking "Introduction to Algebraic Curves" course. Up to now, the only problems i have with this...
Mar22-08 10:17 AM
sylar
0 2,209
I am having difficulties grasping the consequences of this theorem, would really appreciate a little enlightenment. ...
Mar19-08 10:42 PM
mathwonk
8 2,281
Hi, everyone I have studied on a problem for a while on Lie algebras and manifolds. Unfortunately I know very little...
Mar18-08 09:18 AM
saddy
0 1,783
I need to show a particular map f:M-->N is an isometry (globally). M,N are riemannian manifolds, p is a point on M....
Mar16-08 10:34 PM
Cincinnatus
4 6,545
I have a question about Lie subalgebra. They say "a Lie subalgebra is a much more CONSTRAINED structure than a...
Mar16-08 09:53 PM
KarateMan
5 1,655
Can someone explain to me how to go from \Gamma ^k_{ij}=-\bold{e}_j \cdot D_i \bold{e}^k To D_i \bold{e}^k =...
Mar16-08 08:32 PM
hanskuo
2 1,423
Hi, everyone: I am doing some reading on the Frolicher Spec Seq. and I am trying to understand better the...
Mar10-08 01:15 AM
WWGD
5 2,063
Usually the adjoint to the exterior derivative d^* on a Riemannian manifold is derived using the inner product ...
Mar9-08 07:51 PM
HenryGomes
5 3,766
I have a few questions on this topic, and i want to see if i got them partially right or wrong. 1.\pi_1(X,x_0) is the...
Mar8-08 11:01 AM
MathematicalPhysicist
7 1,789
If we have as a manifold euclidian R^2 but expressed in polar coordinates... Do any circle centered at the origin...
Mar6-08 09:32 AM
HallsofIvy
7 3,975

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