# Differential Geometry

- Manifolds. Tensors and forms. Connections and curvature. Differential and algebraic topology
 Views: 524 Announcement: End of year contest, $75+$50 prize! Dec18-13 Meta Thread / Thread Starter Last Post Replies Views Please post any and all homework or other textbook-style problems in one of the Homework & Coursework Questions... Feb23-13 10:25 AM micromass 1 24,711 Hi there: i have a question on geodesics in a Eculidean space equipped with a metric tensor \lambda(x)*I, where I... Nov16-07 11:42 PM WWGD 6 2,393 Hi, I have been reading some stuff about differential geometry (with the ultimate goal of trying to understand loop... Nov16-07 11:27 PM WWGD 13 2,740 somebody know some link or ebook about tensor with examples solved and execises Nov16-07 07:12 PM robphy 1 1,590 Hi, I have some elementary questions about geometry. I often find that I am perfectly able to do calculations, but... Nov14-07 10:10 AM haushofer 14 3,690 Does anybody know how to solve inverse problem ? I mean for some differential 1-forms with several unknown... Nov8-07 06:23 PM Sophus 0 1,042 Hello everyone, I'm new to this forum. I have a doubt about differential forms, related to the divergence. On a... Nov8-07 05:30 PM Sophus 9 2,514 Hi...does anyone have a good description (or a link to it) on geodesic deviation equation?Most of the references i... Nov7-07 01:59 PM Chris Hillman 1 2,870 Hi, I am new to manifold and having a hard time on it. :frown: Could anyone please help me on the following problem.... Nov6-07 08:56 PM Reverie 3 3,702 hi, all, run into one geometry problem: I have two 3-D Cartesian systems, A and B. they share the same original. the... Nov6-07 01:42 PM bigworld005 3 2,998 Curl in arbitrary coordinates ( 1 2 3 ... Last) In differential geometry, the usual curl operation that we are familiar with from elementary calculus is generalized... Nov5-07 10:42 PM mmcf 65 10,975 Let f:M-->N be isometric immersion. Is it true that we can find a curve in f(M) which is geodesic in N? Thanks. Nov5-07 11:21 AM timur 1 2,564 Hi, Let \mathbf{x}(u,v) be a local parametrization of a regular surface. Then the coefficients of... Nov4-07 11:23 PM Chris Hillman 6 5,398 I am sorry never mind this post. Nov4-07 05:06 PM brown042 0 1,784 Hi all, Given a map P: V-->W for vector spaces V and W and the map P*: W* --> V* we have the relationship that... Nov3-07 01:55 PM llarsen 1 2,068 Okay, second question - does anyone know of a good text that covers the basics of manipulating tensors without... Nov1-07 04:22 PM matthewbanar 13 3,926 I think it's accepted to post HW type question in here. "Is there a submersion from S^1 to R? From R to S^1?" ... Oct29-07 07:34 AM Reverie 3 2,182 Why are the tangent vectors of smooth manifolds defined as mappings C^{\infty}(p)\to\mathbb{R} that have the similar... Oct29-07 01:54 AM DeadWolfe 4 1,406 I understand that all rank 2 tensors can be decomposed into a symmetric and a skew symmetric part, but I don't really... Oct29-07 12:52 AM robphy 1 1,473 Hi. I'm considering the covariant derivative \nabla_\mu V^\nu = \partial_\mu V^\nu + \Gamma_{\mu\nu}^\lambda... Oct21-07 08:33 AM CompuChip 4 2,336 To distinguish a critical point is a saddle point or not, It is useful way to use discreminent. The discreminent is... Oct21-07 07:31 AM Reverie 1 2,042 Let w be a 1-form on smooth manifold M. Then is there a vector field X such that locally w(X)=f where f:M-->R... Oct21-07 07:14 AM Reverie 6 1,648 Let M be a three dimensional Riemannian Manifold that is compact and does not have boundary. I believe manifolds that... Oct21-07 06:38 AM Reverie 0 1,915 Hi. I have a question on proof of proposition 2 in chater 7 Spivak volume2. In the proof, he says that the... Oct17-07 07:20 PM joe2317 1 2,255 Let M be a smooth manifold. Locally we can choose 1-forms \omega^{1},\omega^{2},...\omega^{n} whish span M^{*}_{q}... Oct16-07 03:15 PM timur 3 1,513 sorry Please look at next thread. Oct15-07 08:17 PM daishin 0 1,188 delta x (a x b) = (b . delta) a - b (delta . a) + a (delta . b) - (a . delta) b all terms are in vectors, so delta x... Oct11-07 08:23 PM R3DH34RT 7 1,866 If we want to transform vector A from cooedinate ei to ei', then this formula occur: Aj' = aij Ai But I have a... Oct11-07 06:45 PM AlphaNumeric2 4 2,260 I am reading a Vol2 of geometry book by Spivak. On page 220-221 he says that: "Notice that the possibility of... Oct10-07 10:37 PM mathwonk 13 3,818 Let Y_{1},..,Y_{k} be vector fields and let A be a tensor field of type ^{k}_{1}. Could you explain how applying k... Oct7-07 06:12 PM quetzalcoatl9 4 2,292 Re: Foundations of Tensor Analysis for Students of Physics and Engineering with an Introduction to the Theory... Oct7-07 01:40 PM jbowers9 11 2,781 I'm practicing some differential forms stuff and got a bit stuck on something. I'd type it out but the action is very... Oct7-07 08:26 AM AlphaNumeric2 0 2,716 This springs from section 15.1.3 of Superstring Theory (Vol 2) by GS&W (should anyone have that to hand). K is a... Oct7-07 07:43 AM AlphaNumeric2 2 2,663 Where I could find proof of the equivalence of two definitions (by Thomas 0-cocycle... Oct6-07 10:58 AM quintic 0 1,641 I have a known surface \mathbf{r}(s,t) and now I wish to approximate it locally with an ellipsoid (with semi-axes... Oct5-07 04:12 AM geonat 0 1,417 Hi guys, can u please help me in this problem? 1. Evaluate Ai = (Epsilon)ijk bj bk 2. Show that this is... Oct3-07 04:46 AM robphy 18 3,364 I have a following problem. Let D be an operator taking the C^oo functions F to F, and the C^oo vector fields V to... Oct2-07 08:49 PM joe2317 0 1,512 Is there some solved problem book about manifolds? (or where can I find solved problems on manifolds) Oct1-07 11:57 AM robphy 15 4,309 This is a very very simple question and I am sure it will look dumb because I won't be using the correct terminology... Sep20-07 04:51 PM nrqed 7 2,530 First off, I'm no geometer. I've jumped from looking into QFT from an operator algebra perspective to one looking at... Sep18-07 12:58 PM mathwonk 9 4,171 Ok I have been trying to figure this out for a couple of days now and seem to be stumped. I know it is a fairly... Sep15-07 12:56 AM Chris Hillman 1 4,523