# Differential Geometry

- Manifolds. Tensors and forms. Connections and curvature. Differential and algebraic topology
 Views: 8,557 Announcement: Two free ways to get Gold Membership! Jan17-12 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 09:25 AM micromass 1 25,906 Hello, if we consider a diffeomorphism f:M-->N between two manifolds, we can easily obtain a basis for the tangent... Dec7-13 05:37 AM mnb96 0 663 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 04:06 AM bolbteppa 0 635 In Theodore Frankel's book, "The Geometry of Physics", he observes at page 248 that the covariant derivative of a... Dec1-13 02:59 PM center o bass 0 783 I wonder if one should study books like Gauss's General Investigations on Curved Surfaces or Euler's works or there... Nov30-13 02:24 PM mathwonk 1 873 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 10:12 AM center o bass 0 775 cf. Musicals that, unfortunately, would not work. :tongue: I recently started to go a little further in depth into... Nov27-13 05:23 PM R136a1 5 1,439 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 09:55 AM Karamata 0 931 Suppose we have a torsion free connection. Does anyone here know of a slick way to prove that covariant derivatives... Nov24-13 06:12 AM center o bass 1 839 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 07:49 PM lurflurf 4 1,104 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 03:58 PM fzero 1 932 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 05:18 AM center o bass 0 914 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 05:18 AM center o bass 0 834 A p-form ##\alpha## is a completely anti-symmetric tensor. This means that the form is completely determined by a set... Nov16-13 10:58 AM center o bass 2 820 So when we calculate divergence (especially referring to the gauss divergence theorem), why aren't the components of... Nov16-13 09:07 AM HallsofIvy 7 1,103 Hello! I'm currently reading Peskin and Schroeder and am curious about a qoute on page 38, which concerns... Nov13-13 12:37 PM Kontilera 2 950 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 06:39 AM lavinia 5 1,176 Hello, I understand the concepts of real differentiable manifold, tangent space, atlas, charts and all that stuff.... Nov7-13 05:17 PM WWGD 11 1,130 Hi! A proof of Frobenius' theorem (in Schutz Geometrical Methods) uses the fact that if a set of vector fields... Nov7-13 03:37 AM center o bass 0 844 Hi! I have a question about Kähler manifolds. Of course there are many books (I prefer Nakahara) and lecture notes... Nov4-13 01:19 PM Ben Niehoff 2 990 Hello, I notice that most books on differential geometry introduce the definition of differentiable manifold by... Nov4-13 01:12 PM lavinia 4 855 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 07:09 AM mnb96 4 890 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 07:04 PM WWGD 26 1,970 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 07:44 PM WWGD 4 910 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 05:38 PM quasar987 1 825 Hi again: I'm curious as to someone understands well the difference between a Reeb Vector Field and a general... Oct28-13 09:57 PM WWGD 4 987 The standard definition of the lie derivative of X along Y is just (*) \mathcal{L}_YX = \lim_{t\to 0}... Oct28-13 12:14 PM Ben Niehoff 1 822 Hi all, I was wondering where I could learn differential geometry online. Preferably via videos. If anyone could post... Oct26-13 02:49 PM Jorriss 1 1,013 I have just started diving into tensor analysis. To be honest, I didn't know whether to post this question in the... Oct26-13 01:21 AM epr1990 2 1,235 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 12:22 PM R136a1 1 869 Consider a triangulated discrete manifold (a polyhedron) with known vertices (i.e. each vertex is given in terms of... Oct24-13 02:40 AM teodron 0 875 I am reading an article about Minkowski space (as a vector space, which is why I am putting my question in this... Oct23-13 11:34 AM nomadreid 2 893 I've read an article in which a more general version of gauss-codazzi equations are presented namely a version where... Oct18-13 06:19 AM center o bass 0 952 I've been working on a problem where I have to find the geodesics for a given Riemannian Manifold. To present my... Oct17-13 08:39 PM epr1990 1 1,115 What is the least restrictive set of conditions needed to utilize the formula... Oct16-13 05:38 PM Ben Niehoff 4 1,081 i am not sure if this post should be under calculus or not, but i think i'll get a more "complete" answer here. at any... Oct12-13 12:29 PM Mandelbroth 3 1,265 Suppose θ is a differential 1 form defined on a manifold and with values in the Lie algebra of a Lie group,G. On... Oct7-13 09:34 PM lavinia 3 1,258 Hello PF members! I have a problem regarding coordinate and non-coordinate bases. As I understood from my course... Oct7-13 11:27 AM dextercioby 2 898 Suppose we have one polynom ##P(r_1, r_2, \ldots, r_n) = 0## in n complex variables. This defines a n-1... Oct6-13 04:26 AM tom.stoer 3 1,016 Greetings, There is an aspect of tensor-index notation that I want to know more about. For a simple example, let M... Oct4-13 11:42 PM HJ Farnsworth 4 1,151 Hi, I'm new to this forum and I have an application where I want to image an object that is in contact with the... Oct4-13 04:18 PM lferreir 0 855