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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 30,445
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
0 682
I'd like some help understanding three things. - What is the topology of the Grassmann manifold or oriented...
Oct22-10 02:41 PM
13 2,053
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 1,563
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 2,267
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 2,061
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
2 954
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
0 751
Can a connected space have a countable disjoint cover of closed subsets with at least two elements?
Oct21-10 04:43 PM
15 2,244
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 2,106
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 2,188
Show the intersection of complex sphere (|z1|^2+|z2|^2+|z3|^2=1) in C^3 and the complex cone (z1^2+z2^2+z3^3=1) in C^3...
Oct20-10 02:02 PM
1 1,783
"if a vector field has only nondegenerate zeros then the number of zeros is bounded" With no idea how to show that...
Oct20-10 01:42 PM
2 1,750
Hello everyone...I was wondering if it is possible to conceive a 2nd center of a finite sphere in infinity...(I am not...
Oct20-10 07:45 AM
6 1,288
Which of this is tri-conic & which is bi-conic nosecone ...
Oct19-10 08:04 PM
1 1,899
This is not a homework question, although it may appear so from the title. So, in Munkres, Theorem 26.7. says that...
Oct19-10 03:32 PM
2 4,236 Octonions Jonathan Hackett, Louis Kauffman 11 pages, 11 figures (Submitted on 14...
Oct19-10 12:48 PM
16 3,341
Hi I'm trying to solve this exercise "Prove that if C is a circular cylinder with S_1 and S_2 as its boundary...
Oct18-10 04:31 PM
3 1,068
Now F:S^2->R^4 is a map of the following form: F(x,y)=(x^2-y^2,xy,xz,yz) now using the smooth covering map...
Oct18-10 05:58 AM
1 2,561
Any hint PLZ Thank You
Oct18-10 04:32 AM
3 770
How can you find more than one right inverse. Thanks for ur time
Oct17-10 07:25 PM
1 616
Hi, I know that you can determine that the Gaussian curvature of a cone tends to infinity at the vertex, but seeing...
Oct17-10 02:05 PM
7 3,480
The Euler class of the tangent bundle of a compact smooth manifold integrates to the Euler characteristic of the...
Oct17-10 06:11 AM
0 1,032
I just went through and exercise which asks if a product of two path connected spaces is path connected. There...
Oct17-10 06:06 AM
6 2,735
Hello people. In my textbooks the question is asked as following 1. Find the S.D(short distance)between the...
Oct16-10 10:25 AM
4 1,227
I'm a rogue babble master, hear me out. I have been puzzled by this little idea concerning functions and the...
Oct16-10 04:08 AM
1 665
Most definitions I've seen for a manifold are based on the idea that small neighborhoods are homeomorphic to...
Oct15-10 12:34 PM
25 2,497
� R is real line, C is set of Complex numbers If we considered the Euclidean metric on RXR a. Show whether the...
Oct12-10 09:53 AM
1 2,132
(E, B, V) a vector bundle.EndE is the set of endomorphisms of E, then if g belongs EndE therefore g is a linear V-> V...
Oct12-10 06:21 AM
1 747
The information I have on disposal are the coordinates of A, B, the current distance AB=dt and the wished distance...
Oct12-10 03:35 AM
1 831
Metric given by (d) in the textbook on page 48 in the following url. How could we plot this function and characterize...
Oct11-10 10:53 PM
0 1,642
In The Road to Reality, § 20.2, Roger Penrose talks about a "vector field on the phase space T^*(C)", where C is a...
Oct11-10 08:09 PM
2 2,748
Let M1,..,Mk be smooth manifolds, and let Pi_j be the projection from M1XM2X...XMk->Mj. Show that the map...
Oct11-10 07:05 AM
3 831
In R we have the following result: A set C is compact if and only if it is closed and bounded. However, the...
Oct11-10 12:13 AM
14 4,834
Suppose M and N are smooth manifold with M connected, and F:M->N is a smooth map and its pushforward is zero map for...
Oct10-10 10:29 PM
2 2,441
hello friends, i have some point that i didn't understand when i read the article of ALEXEI KOVALEV, if you can help...
Oct10-10 02:08 PM
9 1,222
Hi, It is well known by Varignon's Theorem and the Triangle Inequality that in a convex quadrilateral ABCD with...
Oct10-10 10:17 AM
0 1,437
Hi, It is well known by Varignon's Theorem and the Triangle Inequality that in a convex quadrilateral ABCD with...
Oct10-10 10:10 AM
0 1,104
Hi all, In the paper "Broadband Ground-Plane Cloak" (,...
Oct10-10 02:31 AM
0 764
Hello all, Sometimes I come across the situation that a topology of a space is defined indirectly through some...
Oct9-10 07:57 AM
1 1,784
What is the most convenient way to get a set of unit vectors in N dimensions, such that the angle between two...
Oct9-10 04:25 AM
2 1,015

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