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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 31,092
Just wondering if Traces can be applied to tensors. If the Ricci tensor is Rii then is sums over diagonal elements....
Jan11-10 12:02 PM
7 7,122
I quote Wikipedia: I try to apply this to the natural connection on the tangent bundle of M = S2 (or more...
Jun15-10 10:15 AM
7 2,678
What is a local invariant? For instance, at
Oct14-09 12:26 AM
7 1,644
Any two continuous maps from X to Y, where Y is a convex subset of R^n, are homotopic. For example, the functions f(t)...
Jan13-10 01:46 PM
7 1,951
On page 7 it gives two conditions for a linear function on the space of p-vectors built from a linear function on the...
Jan28-10 06:55 AM
7 2,014
Hello, Suppose that I have a cell complex and I want to define it's geometric realization, I can do it via...
Feb18-10 10:14 AM
7 1,697
What kind of sets exhibit the wada property? I know R2 does but does it extend to R3 or R itself?
Feb23-10 10:28 AM
7 1,353
I'm sorry if this should be in the Analysis forum; I figured it pertained to topology though. Let Y be a subspace of...
Mar2-10 02:43 PM
7 1,540
Hi, everyone: A couple of questions, please: 1) Examples of representative surfaces or curves: Please...
Apr8-10 12:22 AM
7 1,042
Hi, Is it true to say on a topological manifold one can always find a unique metric such that a set of non...
Mar31-10 02:11 AM
7 1,383
Let's denote the ordinary metric with d, so that d(a,b) = \sqrt{(a_1-b_1)^2 + (a_2-b_2)^2}, and then let e denote some...
Mar31-10 05:11 PM
7 2,049
I have seen it mentioned in various places that the Lie algebra of the diffeomorphism group of a manifold M is...
May13-10 02:30 PM
7 3,248
How is a straight line/straight curve defined (in contexts where it is meaningful) ? I am trying to wrap my mind...
May31-10 06:35 PM
7 2,202
I have been asked if the following is true or false the intersection of two connected sets is connected ? I...
Jun5-10 03:02 PM
7 3,049
Hi, everyone: I am trying to find a result for the number of bundles (up to bundle iso.) over a fixed base...
Jun24-10 08:15 AM
7 1,671
Given a smooth manifold with no other structure (like a metric), one can define a derivative for a vector field called...
Jun19-10 12:45 PM
7 1,358
I'm reading Analysis on Manifolds by Munkres and in the section Review of Topology Munkres states the following...
Jun25-10 10:37 PM
7 3,210
Hi i'm using Kreyszig's Introductory Functional Analysis with Applications and he proves that the set of continuous...
Jun27-10 02:44 PM
7 6,849
Hi, Everyone: There is an exercise in the beginning of Bott and Tu's Diff. Forms in Algebraic Topology, of...
Sep20-10 03:20 PM
7 2,883
Quick question: Suppose I have a (transitive) R^n action on a manifold M. If the isotropy group of R^n is discrete,...
Aug30-10 01:50 AM
7 1,389
Like the title says, what is the easiest way to see that CP^1 is topologically just a 2-sphere? Wikipedia says that...
Sep7-10 06:39 AM
7 1,681
I heard this puzzle on the MathFactor podcast (which I highly recommend). If you don't know what Asteroids is...
Sep18-10 08:20 AM
7 1,661
What would a 3D ball look like if it were partially in 4D space when none of the 4th dimension is visible to the 3D...
Oct7-10 01:47 PM
7 2,427
Can anyone tell me a good quotation about topology?
Sep26-10 10:54 AM
7 1,536
I am terribly confused on the issue of trivial tangent bundles. I understand intuitively why some tangent bundles are...
Oct5-10 11:51 AM
7 2,422
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 3,515
OK. Suppose you have a surface with a closed curve as a boundary. Then suppose that surface grows like a soap bubble...
Apr14-04 04:55 PM
8 2,025
On a pseudo-Riemannian manifold we can contract the Riemann curvature tensor to form the Ricci tensor. In this process...
Apr10-06 12:48 PM
8 2,337
Hi we define the projectif space P^n \mathbb{R} by the quotient space :\mathbb{R}^{n+1}/\sim where: x\sim...
Nov10-04 09:25 PM
8 3,037
Is the manifold a space defined by the metric tensor or is it a completetly different thing. I'm new to tensor...
Mar3-05 11:21 AM
8 1,701
Those of you who know me know that my formal education is in physics, not mathematics. So hopefully you'll excuse the...
Mar27-05 05:24 PM
8 3,908
Hello I have a small pb: Let \displaystyle{M=\mathbb{R^{2}\{(x,y);x=0\quad ou \quad y=-1} Let D such that ...
Apr6-05 08:57 PM
8 2,684
What are differential forms? Is this what I'm gonna learn about in my upcoming differential geometry class?
May9-05 02:58 PM
8 3,538
Hello. I was wondeirng if anyone knew any good textbooks on Differential Geometry for independent study, at an...
Sep9-05 12:25 AM
8 4,580
First of all, I'm not sure if this is the right forum, but none of the forums mention topology in their description. ...
Nov28-05 03:54 PM
matt grime
8 5,062
I would welcome the parametric equations for an embedding in R3 of a locally Euclidean Möbius Strip without self...
Dec23-05 12:19 PM
8 2,547
I'm encountering the gradient of a vector field in a problem at the moment. Not the divergence, specifically the...
Nov14-06 01:36 PM
8 20,224
Can anyone point me to good reference that fully develops the geometry of geodesic curvature? Most of the ones I have...
Oct2-06 05:17 AM
8 8,843
I just finished learning the fundamental theorem of curves in 3 dimensions. As a reminder, this is the theorem that...
Dec1-06 04:31 PM
Chris Hillman
8 2,174
I'm reading "tensor analysis on manifolds" by Bishop and Goldberg. I have taking a course in differential geometry i...
Nov21-06 08:54 AM
8 3,275

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