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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 30,268
Hi all! It's already a couple of days that I'm trying to solve this problem. I've been given the following Kahler...
Jul8-12 04:37 AM
3 1,085
On page 333 in Section 52: The Fundamental Group (Topology by Munkres) Munkres writes: (see attachement giving Munkres...
Jul7-12 09:06 AM
3 1,176
This thread asks for help calculating the Z2 cohomology ring of the Klein bottle using intersections. This is what...
Jul7-12 08:07 AM
3 1,707
Can someone explain to me in detail, why the ratio of the circumference of a circle to its diameter is not equal to pi...
Jul5-12 05:46 PM
11 1,679
I'm not sure if this is the right section, but what the hell. I've been looking to buy a blu-ray of fractal zooms,...
Jul5-12 02:55 PM
0 745
There is a part in the proof of sard's theorem where we restrict our discussion to a point x such that Df(x)=0, and...
Jul5-12 02:53 PM
1 961
I am reading Thurston's book on the Geometry and Topology of 3-manifolds, and he describes the metric in the Poincare...
Jul5-12 02:25 PM
4 1,499
Hello, In R^3, the surface of the parallelogram determined by two vectors u and v is given by the norm of the cross...
Jul4-12 02:24 PM
26 1,905
Hi! Does anyone know which is exactly the map of groups (2,3,∞) → (2,3,n) (from modular group to triangle group) as...
Jul4-12 07:25 AM
0 687
Hello, I want to ask for a verification of something I did. Lets say I want to compute the m-th cohomology group of...
Jul3-12 08:35 PM
3 1,569
I think this a map of the Klein four-group geometry. Comments?...
Jul3-12 07:36 PM
57 9,021
Dear all, I have a problem that I need to solve. (I have made posts previously about this as well). Quite simply...
Jul2-12 11:28 PM
1 1,349
consider we have n dimensional manifold,N at point p we can define a vector this vector is independent of our...
Jul1-12 06:07 PM
1 591
{(a_i)_j} is the dual basis to the basis {(e_i)_j} I want to show that ((a_i)_1) \wedge (a_i)_2 \wedge.... \wedge...
Jun28-12 03:16 PM
1 798
Desargues' theorem: Two triangles are in perspective axially if and only if they are in perspective centrally. I...
Jun26-12 05:10 PM
0 793
Hi, I hope this is not too ignorant, but my Algebraic Topology is rusty: Is there such a thing as DeRham...
Jun26-12 07:30 AM
10 2,908
Hi all! I have some problems understanding the geometrical construction of Klein's quartic. Starting from the...
Jun25-12 04:12 PM
1 1,116
Hi! I'm trying to understand a proof for the fact that the isometry group of a symmetric space is a Lie group. The...
Jun25-12 02:51 PM
0 727
Hello, I'm trying to define an axis as a set of 3 unit vectors--u, v, and w. at a given point P Suppose we are...
Jun25-12 09:16 AM
3 1,525
Consider the following: On a circle of radius 1, two points are marked: P1 and P2. Two lines are drawn from the...
Jun24-12 07:27 PM
1 888
hi friends !! i have a little problem : Let M and N be two varieties, such that N is a menu hermitian metric h. Let...
Jun24-12 03:48 PM
0 802
Hi! I'm trying to give a few examples of symmetric manifolds. In the article "Introduction to Symmetric Spaces and...
Jun24-12 05:40 AM
6 1,675
Hello everyone, Let r(u_i) be a surface with i=1,2. Suppose that its first fundamental form is given as ds^2...
Jun23-12 12:46 PM
8 1,878
Hi! Suppose we have a topological space X, a point x\in X and a homomorphism \rho:\pi(X,x) \rightarrow S_n with...
Jun23-12 12:46 PM
3 1,200
Rao: Topology: Proposition 1.2.4. If (X,T) is a topological space, a subset A of X is closed iff the the derived set...
Jun19-12 10:47 PM
1 1,044
My question is mainly concerned with discovering the allowable set of "configurations" of the given problem: We...
Jun18-12 01:57 PM
0 843
I am looking for a theorem that states approximately the following: An n-dimensional object, while appearing...
Jun18-12 11:40 AM
0 815
I am working on a Matlab sim and I need to find the shorted distance of a point to an Elliposid surface. The point...
Jun18-12 09:00 AM
1 1,241
consider t is arbitrary tensor and is Lie derivative how can we show that Lt=Lx Ly t - Ly Lx t
Jun18-12 03:58 AM
1 1,146
Let RP2 denote the real projective plane (it can be obtained from glueing a Mobius band and a disk whose boundary is...
Jun17-12 02:02 PM
23 4,123
I'm reading a paper and have came across the term 'Cn-close' in the sense of a curve being C1-close to a circle for...
Jun17-12 01:12 PM
1 968
Hi ALL, I'm glad I found this Forum. I'm an engineer, rusty with my math, building a practical prototype sensor...
Jun17-12 10:51 AM
0 676
Hello! Is any covariant vector orthogonal to absolute derivative of its contravariant counterpart? I read a GR...
Jun16-12 09:58 PM
1 976
maybe its simple permutation and combination technique... I ve tried to resolve it on my own but I couldn't...The...
Jun16-12 09:35 PM
4 1,071
I know the following |x|-|y| \leq |x+y| \leq |x| + |y| where does |x-y| fit in the above equation?
Jun16-12 09:28 AM
5 1,425
Hi all! Can you please guide me how to find the quadrature point of a pentagonal cell elements.
Jun15-12 09:18 AM
Prabhat Kumar
0 850
"Let f,g:Sn→Sn be maps so that f(x) and g(x) are not antipodal for any x. Show that f and g are homotopic." Here's...
Jun15-12 01:55 AM
8 1,657
Hello! I'm currently reading John Lee's books on different kinds of manifolds and three questions has appeared. In...
Jun14-12 12:59 AM
4 1,926
What does orbifold means? The wikipedia article says it is a generalization of manifolds which looks like a quotient...
Jun13-12 08:28 PM
10 2,119
Prove or disprove that f is a quotient mapping. f:R^3\{(x1,x2,x3):x1=0}--->R^2 defined by ...
Jun13-12 01:26 PM
3 1,143

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