Differential geometry Definition and 409 Threads

Hello, I am learning General Relativity through some books like 'Gravity' by Hartle and through some other textbooks. All those books, do not speak of general relativity from the context of differential geometry. I have a fair amount of knowledge of calculus as well as set theory. My...

Homework Statement Show that for any trajectory r(t) the acceleration can be written as: \mathbf{a}(t)=\frac{dv}{dt}\hat{T}(t)+\frac{v^2}{\rho}\hat{N}(t) where v is the speed, T is a unit vector tangential to r and N is a unit vector perpendicular to T, at time t. rho is the radius of...

I am a 3rd year mechanical engineering student at LSU, but my true interest lies in theoretical physics and mathematics (specifically general relativity and differential geometry). I've taken calculus 1,2,3, linear algebra, ordinary differential equations, number theory, discrete math, and...

Hi, I was wondering if someone know of a solution book for this book, I'm studying for final, having lot of problem with this class... (not my type of math I guess!) Thanks

I'm a physics major interested in taking some upper level math classes such as topology, differential geometry, and group theory but these classes are only taught in the math department and are heavy on the proofs. Analysis are recommended and preferred prerequisites but are apparently not...

Homework Statement Using the curve \vec{a}(u,v)= (u,v,uv) for all (u,v) ε R^2 Find the matrix for d\vec{N} in the basis of {\vec{a}_{u},\vec{a}_{v}} Homework Equations Well first off i found the partial derivatives \vec{a}_{u} which is 1,0,v, while \vec{a}_{v} is 0,1,u Then using those...

Hi all, I was wondering where I could learn differential geometry online. Preferably via videos. If anyone could post any links to free sites it would be much appreciated. Thanks in advance.

A few topics we are covering in class are: Gauss map, Gauss curvature, normal curvature, shape operator, principal curvature. I am having difficulty understanding the concepts of curves on surfaces. For example, this problem: Define the map ##\pi : (\mathbb{R}^3-\{(0,0,0)\})\to S^2## by...

I am reading Spivak, Calculus on manifolds, and I have a basic working knowledge of topology through Mendelson, "Introduction to Topology", I want to learn more about differential geometry, especially co variant derivatives, levi-civita connections, Ricci and Rieman curvature tensors. I know...

I've been wanting to see what this topic is all about for awhile now. I see the word "Manifold" and other terminology floating around on the forum. It got me really curious. I wonder what the prerequisites are to reading a book like this? Hypothetically I have the prerequisites, what would...

Hi! I'm trying to read up on the subject of hypersurfaces related to GR; First and second fundamental form, Theorema Egregium etc.. Does anyone know any good treatments? (Books or notes)

Homework Statement Hello, I posted a similar question in the physics section but no one was able to help, I am first going to include a link to the older problem where I was attempting to find the ,(Finding the local flat space of the Poincare half disk metric), and explain what is different...

Does it still have a sense of Euclid-style geometry-are there still cubes and spheres, so to speak? Is it mostly about 1D curves/2D surfaces, or does it consider higher dimensions? Are the surfaces which the field concerns mostly graphs of several variables, e.g. ## x^3+y^3+z^3=1 ##, or are they...

Author: Barrett O'Neill Title: Elementary Differential Geometry Amazon Link: https://www.amazon.com/dp/0120887355/?tag=pfamazon01-20 Prerequisities: Contents:

Is it necessary to finish Spivak's little book to move on to Spivak's Differential Geometry I, or is the material on differential forms and integration on manifolds in Chapter's 4 and 5 of Spivak's little book covered in Differential Geometry I?

Hello, I am new very new in this subject. I have a curiosity in understanding diff.geometry. I have some questions (which might sound elementary) to ask: (1) Is diff.geometry a subject related to the study of surface, curvatures, manifolds? (2) How it is different from Euclidean geometry...

Hello, I am a beginner. I am self taught in differential calculus. Can you please suggest me any book, as a beginner, to have a very basic idea and overview on Differential Calculus. Any free e-book? Kindly suggest.

Homework Statement Let α(t) be a regular, parametrized curve in the xy plane viewed as a subset of ℝ^3. Let p be a fixed point not on the curve. Let u be a fixed vector. Let θ(t) be the angle that α(t)-p makes with the direction u. Prove that: θ'(t)=||α'(t) X (α(t)-p)||/(||(α(t)-p)||)^2...

Hi, I read in Padmanabhan's book that \nabla_a J^a=0 implies that there exists an antisymetric tensor P such that J^a= \nabla_b P^{ba}. What's the name of the theorem? Any reference? Thanks

Suppose x(t) is a curve in ℝ^2 satisfying x*x'=0 where * is the dot product. Show that x(t) is a circle. The hint says find the derivative of ||x(t)||^2 which is zero and doesn't tell me much. I was hoping for x*x= r, r a constant.

Hi there. I want to learn some differential geometry on my own, when I find some time. My intention is to learn the maths, so then I can get some insight, and go more deeply on the foundations of mechanics. I need to start on the basics. I had some notions on topology when I did my analysis II...

the differential geometry is so abstract to understand. All are terms and theorem. How to understand it? can someone give me some method and guidance to learn it. HELP!

Author: Serge Lang Title: Fundamentals of Differential Geometry Amazon Link: https://www.amazon.com/dp/038798593X/?tag=pfamazon01-20 Prerequisities: Grad Analysis, Differential Geometry Level: Grad Table of Contents: Foreword Acknowledgments General Differential Theory Differential...

Author: William Burke Title: Applied Differential Geometry Amazon Link: https://www.amazon.com/dp/0521269296/?tag=pfamazon01-20 Prerequisities: Level: Undergrad Table of Contents: Preface Glossary of notation Introduction Tensor in linear spaces Linear and affine spaces...

Author: Michael Spivak Title: A Comprehensive Introduction to Differential Geometry Amazon Link: https://www.amazon.com/dp/0914098705/?tag=pfamazon01-20 https://www.amazon.com/dp/0914098713/?tag=pfamazon01-20 https://www.amazon.com/dp/0914098721/?tag=pfamazon01-20...

Author: C.J. Isham Title: Modern Differential Geometry for Physicists Amazon Link: https://www.amazon.com/dp/9810235623/?tag=pfamazon01-20 Table of Contents: An Introduction to Topology Preliminary Remarks Remarks on differential geometry Remarks on topology Metric Spaces The...

How important is differential geometry in physics? Can someone give me some applicable fields?

in a nutshell, what is the difference between those two fields?

The context of this question is looking at straggling in plasma. I was told there was a simple differential geometry relationship between the following entities: dE/dx, dE/dy and dE/dt, where x,y are distance in perpendicular directions (axes on a plane), t is time and I'm using E to...

I want to study algebraic geometry and differential geometry, what should I learn beforehand what is the relation between abstract algebra and homological algebra:confused:

Hello everyone! I just wanted to ask a question about how I should study for differential geometry. Now, as I have it, I've got a few suggestions for books, of which two stand out prominently: 1. John Lee's Introduction to smooth manifolds 2. De Carmo Which one would be best for self study...

As the title says. Can anyone recommend me some good books for differential geometry(preferably ones with proofs and examples/exercises)?

hey all, in this book ; https://www.amazon.com/Geometry-Riemannian-Spaces-Lie-Groups/dp/0915692341/ref=sr_1_1?ie=UTF8&qid=1348590926&sr=8-1&keywords=geometry+of+riemannian+++spaces++cartan On page 178 ( which I attach a snapshot of it) Cartan had introduced a formula (see in the snapshot...

Hi everyone, I was wondering if I could some advice from anyone who has some experience with higher level general relativity. Any help would be greatly appreciated! Some background: I'm currently working through Robert Wald's General Relativity and am struggling a lot with the "advanced...

My teacher has defined U_1 = \langle1, 0, 0\rangle, U_2 = \langle0, 1, 0\rangle, and U_3 = \langle0, 0, 1\rangle. So it seems like the function maps L(\langle1, 0, 0\rangle, \langle0, 1, 0\rangle) = a, L(\langle1, 0, 0\rangle, \langle0, 0, 1\rangle) = b,, and L(\langle0, 1, 0\rangle...

The title says everything. Can a mathematician do fruitful research in general relativity if he masters differential geometry and manifolds?

Are there any good papers or books that go over our current understanding of differential geometry for 2-dimensional complex spaces? Hermitian vs anti-symmetric metric tensors, dealing with complex conjugates, and defining affine connections? Yes, I've already hit up Google, so I was hoping...

This is the course description: I want to take this class because the professor comes highly recommended, but I'm a little worried that I won't be entirely prepared for it. Normally this class requires Real Analysis as a prerequisite, and even though the professor explicitly states that...

What books should I read as prerequisites for Spivak's Differential Geometry Series? Trying to pick up Diff Geom for graduate physics but right now it is pretty daunting. I've got single variable calculus and linear algebra under my belt. Just looking for bare minimum requirements here to...

I have to choose which math course I'm going to take next term. I want to take both but I'm already taking two physics courses and my college's distribution requirements require that I take an English next term... bleh... I could audit one of the physics and then take both math courses, but that...

Hi all, I've been wondering about this for some time. While I am only familiar with the basics of differential geometry, I have come across the Lie bracket commutator in a few places. Firstly, what is the intuitive explanation of the Lie bracket [X,Y] of two vectors, if there is one? In...

Hello Everyone, I am just wondering what the difference in these is. Could someone please give a brief example of non-coordinate based differential geometry vs the equivalent in coordinate based, or explain the difference (whichever is easier)? Also, what advantages does one have over the...

I am an Astrophysics undergrad, and will be taking Classical Differential Geometry I & II. Are there any classes that will make understanding Differential Geometry easier. I can chose from: -Introduction To Abstract Algebra -Introduction To Mathematical Analysis -Introduction To Real...

http://digi-area.com/DifferentialGeometryLibrary/ includes over 580 objects for differential geometry and its applications. Moreover here is 380 Exact Solutions of Einstein's Field Equations. The formulas are represented in different forms: metric from, Contravariant Newman–Penrose Tetrad...

I have decided to attempt to pick up some differential geometry on my own, and I am trying to get some traction on the subject which I do by trying to reduce it to familiar and simple cases. This is a trivial case, I know, but it will go a long way in advancing my understanding. Suppose the...

Homework Statement Homework Equations L[c]:=\int_{a}^{b}(\sum_{i,j=1}^{2}g_{ij}(c(t))c_{i}'(t)c_{j}'(t))^{1/2}dt The Attempt at a Solution So g_{ij}(x,y)=0 for i{\neq}j, c_{1}'(t)=-Rsin(t), c_{2}'(t)=Rcos(t) so...

So I took an analysis class which covered chapters 9 and 10 of Rudin's PMA, for those of you who don't know that's multivariable analysis and differential forms, and I have taken a course in vector calculus but never a proper course on differential geometry. Thus my introduction to the subject...

Hi all , How can I find lecture notes on ArXiv ? I was looking for lecture notes on Yang-mills theories treated in the language of differential geometry but didn't succeed till now . Can some one recommend me some good resource for it?

Hello. I'm new here and I'm not sure if I should post this topic here or in general math, or anywhere else. Feel free to move the topic elsewhere if needed. Just a bit of explanation first. I'm not from USA (so forgive any grammar errors) and I don't understand completely your academic...

My university is offering a Differential Geometry course next semester and while I am interested in the subject, I do not plan to take the class unless it has practical use for me. I have no interest in doing theoretical work. Does differential geometry serve any use to applied physics/engineering?