Differential Geometry

- Manifolds. Tensors and forms. Connections and curvature. Differential and algebraic topology
 Views: 70 Announcement: PF Member Award voting is open! Dec12-13 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 24,617 So, by accident, while deriving the induced metric for a sphere in 3 dimensions I realized that the transpose of the... Y 04:25 PM Ben Niehoff 5 206 Sorry if this question seems too trivial for this forum. A grad student at my university told me that a compact... Dec10-13 11:09 AM Sajet 2 194 Hi. I studied calculus a while back but am far from a math god. I have been reading around online about hyperbolic... Dec9-13 12:48 PM Reuel 2 284 hi all! I have a problem related with some data analysis. I have two functions, expressin the energy resolution of... Dec8-13 08:57 AM 1Keenan 0 212 Is there a rigorous integral definition of the exterior derivative analogous to the way the gradient, divergence &... Dec7-13 10:37 PM Mandelbroth 3 314 Hello, if we consider a diffeomorphism f:M-->N between two manifolds, we can easily obtain a basis for the tangent... Dec7-13 06:37 AM mnb96 0 146 How do I visualize \dfrac{xdy-ydx}{x^2+y^2}? In other words, if I visualize a differential forms in terms of... Dec7-13 05:06 AM bolbteppa 0 124 In Theodore Frankel's book, "The Geometry of Physics", he observes at page 248 that the covariant derivative of a... Dec1-13 03:59 PM center o bass 0 262 I wonder if one should study books like Gauss's General Investigations on Curved Surfaces or Euler's works or there... Nov30-13 03:24 PM mathwonk 1 308 Suppose that we have an (n+m)-dimensional tangent space ##T_p^{n+m}## which we decompose into the direct sum of two... Nov28-13 11:12 AM center o bass 0 295 cf. Musicals that, unfortunately, would not work. :tongue: I recently started to go a little further in depth into... Nov27-13 06:23 PM R136a1 5 919 How to deduce is it \{\cos(\sqrt{2}t)(2+\cos t), \sin(\sqrt{2}t)(2+\cos t),\sin t \mid t \in \mathbb{R}\} submanifold... Nov24-13 10:55 AM Karamata 0 460 Suppose we have a torsion free connection. Does anyone here know of a slick way to prove that covariant derivatives... Nov24-13 07:12 AM center o bass 1 307 I'm sorry if this is in the wrong place but I believe the answer is geometric in nature somehow. So as a young... Nov23-13 08:49 PM lurflurf 4 655 Say we have two vector fields X and Y and we form the projection of Y, Y' orthogonal to X. Since every vector field is... Nov19-13 04:58 PM fzero 1 468 Suppose we are given two projection operators H' and H'' such that H' + H'' = 1, i.e. that any vector can be written... Nov18-13 06:18 AM center o bass 0 489 Suppose we are given two projection operators H' and H'' such that H' + H'' = 1, i.e. that any vector can be written... Nov18-13 06:18 AM center o bass 0 413 A p-form ##\alpha## is a completely anti-symmetric tensor. This means that the form is completely determined by a set... Nov16-13 11:58 AM center o bass 2 412 So when we calculate divergence (especially referring to the gauss divergence theorem), why aren't the components of... Nov16-13 10:07 AM HallsofIvy 7 633 Hello! I'm currently reading Peskin and Schroeder and am curious about a qoute on page 38, which concerns... Nov13-13 01:37 PM Kontilera 2 518 I'm reading "Mirror Symmetry" by Hori et al. In it, they compute the cohomology groups for the sphere and the torus. I... Nov8-13 07:39 AM lavinia 5 775 Hello, I understand the concepts of real differentiable manifold, tangent space, atlas, charts and all that stuff.... Nov7-13 06:17 PM WWGD 11 697 Hi! A proof of Frobenius' theorem (in Schutz Geometrical Methods) uses the fact that if a set of vector fields... Nov7-13 04:37 AM center o bass 0 491 I have read statements like "assume that there exists a killingvector ##\xi## that makes it possible to compactify the... Nov6-13 02:32 PM George Jones 7 1,023 Hi! I have a question about Kähler manifolds. Of course there are many books (I prefer Nakahara) and lecture notes... Nov4-13 02:19 PM Ben Niehoff 2 609 Hello, I notice that most books on differential geometry introduce the definition of differentiable manifold by... Nov4-13 02:12 PM lavinia 4 530 Hello, I read from several sources the statement that the set of points M\inℝ2 given by (t, \, |t|^2) is an example... Nov4-13 08:09 AM mnb96 4 582 Hi, All: Let w be a contact form , say in ℝ3, or in some 3-manifold M i.e., a smooth, nowhere-integrable 2-plane... Nov3-13 08:04 PM WWGD 26 1,374 Hello, I was wondering if it is true that any open subset Ω in ℝn, to which we can associate an atlas with some... Nov1-13 08:44 PM WWGD 4 607 I want to show that if G is a smooth manifold and the multiplication map m:G×G\rightarrow G defined by m(g,h)=gh is... Oct30-13 06:38 PM quasar987 1 589 Hi again: I'm curious as to someone understands well the difference between a Reeb Vector Field and a general... Oct28-13 10:57 PM WWGD 4 719 The standard definition of the lie derivative of X along Y is just (*) \mathcal{L}_YX = \lim_{t\to 0}... Oct28-13 01:14 PM Ben Niehoff 1 582 Hi all, I was wondering where I could learn differential geometry online. Preferably via videos. If anyone could post... Oct26-13 03:49 PM Jorriss 1 731 I have just started diving into tensor analysis. To be honest, I didn't know whether to post this question in the... Oct26-13 02:21 AM epr1990 2 932 I'm trying to come up with a simple proof that if M is an embedded submanifold of N, and P is an embedded submanifold... Oct24-13 01:22 PM R136a1 1 628 Consider a triangulated discrete manifold (a polyhedron) with known vertices (i.e. each vertex is given in terms of... Oct24-13 03:40 AM teodron 0 692 I am reading an article about Minkowski space (as a vector space, which is why I am putting my question in this... Oct23-13 12:34 PM nomadreid 2 692 I've read an article in which a more general version of gauss-codazzi equations are presented namely a version where... Oct18-13 07:19 AM center o bass 0 776 I've been working on a problem where I have to find the geodesics for a given Riemannian Manifold. To present my... Oct17-13 09:39 PM epr1990 1 842 What is the least restrictive set of conditions needed to utilize the formula... Oct16-13 06:38 PM Ben Niehoff 4 863