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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 30,178
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 6,803
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 2,845
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 1,371
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 1,647
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 1,651
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 2,416
Can anyone tell me a good quotation about topology?
Sep26-10 10:54 AM
7 1,526
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 2,294
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 3,473
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 2,008
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 2,308
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 3,027
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 1,687
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 3,773
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 2,672
What are differential forms? Is this what I'm gonna learn about in my upcoming differential geometry class?
May9-05 02:58 PM
8 3,460
Hello. I was wondeirng if anyone knew any good textbooks on Differential Geometry for independent study, at an...
Sep9-05 12:25 AM
8 4,539
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 5,015
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 2,522
Hi everybody, How can one show that the tangent bundle TS² of the 2-sphere is not trivial ? I know we can use the...
Mar3-09 08:32 AM
8 6,879
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 20,140
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 8,680
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 2,145
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 3,247
Hello, I am doing a project on Riemann but I don't understand some of his contributions. For instance, I do not...
Feb4-07 07:51 PM
8 1,750
Is it true that f is a continuous function from A \times B to C (A, B, C are topological spaces) if and only if...
Aug11-07 10:56 AM
8 2,229
My professor recently defined immersions and embeddings in class, but he didn't really make any attempt to motivate...
Apr8-08 03:10 PM
8 2,879
Hi, everyone: I was just going over some work on Hyperbolic geometry, and noticed that the geodesics in...
Dec9-07 04:23 PM
Chris Hillman
8 5,768
I need to prove that for every continuous function f:X->X of a metric and compact space X, which satisfy for each two...
Feb16-08 11:30 AM
8 2,757
I am having difficulties grasping the consequences of this theorem, would really appreciate a little enlightenment. ...
Mar19-08 10:42 PM
8 2,348
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 2,339
Let M be a compact manifold and C(M), C^{\infty}(M) denote rings of continuous (resp. smooth) real functions on M. Let...
May8-08 03:14 PM
8 2,122
I'm reading this book on modern geometry and I was wondering if I'm doing these problems right: if I'm give a...
Oct4-08 06:21 AM
8 4,724
Hey guys, How exactly do you take the trace of a tensor product? Do I take the trace of each tensor individually...
Nov21-08 06:25 AM
8 6,574
Let's take a simple example. Both a cylinder and Möbius strip consist of a circle with a line segment associated...
Nov23-08 06:49 AM
8 2,191
Show that any basic open set about a point on the "top edge," that is, a point of form (a, 1), where a < 1, must...
Dec8-08 07:42 PM
8 2,627
Hi, everyone : I read a problem posted somewhere else on showing that, "for the correct value m-- an integer"...
Mar9-09 01:15 AM
8 2,118
We saw in the thread Definition of arc length on manifolds without parametrization that arc length that is usually...
Mar18-09 03:03 AM
8 1,819
What fields of interest in topology (or else) should I learn to fully understand his proof? Is there a comprehensible...
Apr14-09 07:10 AM
8 2,661
Question: Let M, N be orientable closed n-manifolds. Knowing that the nth homology group of an orientable closed...
Apr15-09 04:21 AM
8 4,457

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