# Differential Geometry

- Manifolds. Tensors and forms. Connections and curvature. Differential and algebraic topology
 Meta Thread / Thread Starter Last Post Replies Views Views: 1,472 Announcement: Follow us on social media and spread the word about PF! Jan16-12 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 31,063 In Frankel's book he writes that in R^{3} with cartesian coordinates, you can always associate to a vector \vec{v} a... T 09:14 AM Greg Bernhardt 1 198 Hey JO, I'm reading a book on geometric algebra and in the beginning (there was light, jk) a simple calculation is... Y 03:33 PM JonnyMaddox 5 228 Does anybody know nice introductory material for K3 manifold/ surface? Some very basic exposition, maybe hidden in... Aug24-14 12:35 AM mathwonk 2 2,130 Let me say from the beginning I'm not talking about the non-coordinate unit vectors for polar coordinates. I'm talking... Aug22-14 08:40 PM Fredrik 3 194 Alright, so I was reading up on tensors and such with non-Cartesian coordinate systems all day but now I'm a bit tired... Aug22-14 07:53 AM JonnyMaddox 5 187 What are tensors? Aug21-14 02:03 PM Blazejr 6 413 Hello. I'm learning about Lie derivatives and one of the exercises in the book I use (Isham) is to prove that given... Aug21-14 05:50 AM Matterwave 5 235 i really try understand these initial concepts before continue my work, The necessity to use contra/covariants... Aug20-14 02:15 PM Matterwave 5 269 i'm looking for a curve that would have a shape of a snowdrop (the white spring flower) in 3D space. i have tried some... Aug20-14 05:19 AM ann96 2 197 Hi all, I am trying to describe/understand how to define a 2-plane distribution in R^3 , i.e., an assignment of a... Aug20-14 03:51 AM Pond Dragon 3 211 Hello I've been reading some Group theory texts and would like to clarify something. Let's say we have two Lie groups... Aug18-14 01:27 PM Matterwave 2 236 Dear all, I was revising on a bit of tensor calculus, when I stumbled upon this: \delta^i_j = \frac{\partial... Aug16-14 01:32 PM Matterwave 2 237 I have a cluster of voxels and a 2nd order stress tensor corresponding to each voxel. I was wondering as to what would... Aug15-14 05:19 PM AlephZero 1 210 does anyone have a proof of this? Aug14-14 07:00 PM mathwonk 2 355 The Maurer-Cartan one-form ##\Theta = g^{-1} dg## is though of as a lie algebra valued form. It arises in connection... Aug12-14 03:57 PM Greg Bernhardt 1 466 Hi, I have real problems with the indices here, can someone give me a step by step explanation how to compute stuff... Aug12-14 03:07 PM Geometry_dude 5 1,003 Can somebody explain to me what is a manifold.Also what it means for a space to be curved and how we define... Aug11-14 05:05 PM mathwonk 12 773 Hello, the tensor product definition of a two form is \alpha^{1} \wedge \beta^{1} := \alpha \otimes \beta - \beta... Aug8-14 06:26 PM JonnyMaddox 10 409 In the formulation of connections on principal bundles, one derives an expression for the covariant exterior... Aug7-14 11:41 AM center o bass 4 353 I have an object (A) at some altitude above the Earth ellipsoid, and a point (B) on the surface of the Earth. ... Aug6-14 12:11 AM GreenLRan 6 910 Hi all, I'm trying (and failing miserably) to understand tensors, and I have a quick question: is the inner product... Aug4-14 11:17 AM 21joanna12 4 502 It is pretty straight forward to prove that the Kronecker delta \delta_{ij} is an isotropic tensor, i.e. rotationally... Aug1-14 08:32 PM lpetrich 6 530 Hi, I'm giving a talk tomorrow morning, and I'd like to use the following fact: a path-connected subgroup of SO(3)... Jul31-14 12:05 PM micromass 3 444 I finally finished my big summer research project. Reviewing how it went, it is clear to me that I lack an... Jul24-14 09:14 PM Pond Dragon 1 1,247 Hey guys, I'm working on a summer research project right now in diff. geo. I'm at the point where I have to define the... Jul23-14 11:35 PM Greg Bernhardt 1 2,101 In Nakahara's book, the interior product is defined like this : i_{x} \omega = \frac{1}{r!} \sum\limits_{s=1}^r... Jul22-14 07:50 PM JonnyMaddox 11 2,579 I wonder if curvature necessarily means space has been removed. The typical example is forming a "curved" surface by... Jul22-14 02:31 AM WWGD 9 990 (From another site) I think the answer is no, for ##i: S \rightarrow \mathbb R^n ## the inclusion/restriction, and... Jul18-14 05:48 PM WWGD 3 1,477 I'm trying to explicitly show that \varepsilon^{0 i j k} \varepsilon_{0 i j l} = - 2 \delta^k_l I sort of went... Jul18-14 09:11 AM Emil 2 1,409 Long time reader, first time poster. Originally, it was my contention that all Lie groups could be written as the... Jul17-14 10:36 PM Pond Dragon 1 1,381 I need to use a computational software to work on tensorial hermite polynomials. The operations I want to perform are... Jul9-14 08:46 AM parulm 3 3,169 Hello, I'm trying to get a hang of the defintion presented in Arfken - Mathematical Methods for Physicists for 3... Jul8-14 02:46 AM electricspit 2 1,967 I am working on a paper that provides the following formula for computing radius of curvature at a point on a surface.... Jul4-14 10:39 AM mathwonk 1 3,493 I'm reading about multlinear algebra and I'm stuck at differential form and outer product. The definitions involve... Jul4-14 12:33 AM WWGD 13 4,267 Greetings, I am attempting to compute geodesic distances on manifolds where structural data have been sparsely... Jul1-14 10:15 PM Greg Bernhardt 1 2,452 Hi, I have an exercise whose solution seems too simple; please double-check my work: We have a product manifold... Jul1-14 10:15 PM Greg Bernhardt 1 2,536 Suppose we have a foliation of leaves (hypersurfaces) with codimension one of some Riemannian manifold ##M## with... Jun27-14 07:56 AM Geometry_dude 2 4,052 Suppose one has a foliation of a manifold ##M## with codimension one leaves that are all isometric. What is such a... Jun27-14 06:35 AM Geometry_dude 3 2,930 I'm looking to prove the Global Frobenius theorem, however in order to do so I need to prove the following lemma: ... Jun26-14 10:37 PM Greg Bernhardt 1 2,651 A scalar field can be the exact form of a vector field (potential form)? It's make sense? Jun26-14 03:38 PM Geometry_dude 7 2,861