Smooth functions | Maps of manifolds | Differential geometry | Connection (mathematics)
In the mathematical field of differential geometry, a Cartan connection is a flexible generalization of the notion of an affine connection. It may also be regarded as a specialization of the general concept of a principal connection, in which the geometry of the principal bundle is tied to the geometry of the base manifold using a solder form. Cartan connections describe the geometry of manifolds modelled on homogeneous spaces. The theory of Cartan connections was developed by Élie Cartan, as part of (and a way of formulating) his method of moving frames (repère mobile). The main idea is to develop a suitable notion of the connection forms and curvature using moving frames adapted to the particular geometrical problem at hand. In relativity or Riemannian geometry, orthonormal frames are used to obtain a description of the Levi-Civita connection as a Cartan connection. For Lie groups, Maurer–Cartan frames are used to view the Maurer–Cartan form of the group as a Cartan connection. Cartan reformulated the differential geometry of (pseudo) Riemannian geometry, as well as the differential geometry of manifolds equipped with some non-metric structure, including Lie groups and homogeneous spaces. The term 'Cartan connection' most often refers to Cartan's formulation of a (pseudo-)Riemannian, affine, projective, or conformal connection. Although these are the most commonly used Cartan connections, they are special cases of a more general concept. Cartan's approach seems at first to be coordinate dependent because of the choice of frames it involves. However, it is not, and the notion can be described precisely using the language of principal bundles. Cartan connections induce covariant derivatives and other differential operators on certain associated bundles, hence a notion of parallel transport. They have many applications in geometry and physics: see the method of moving frames, Cartan formalism and Einstein–Cartan theory for some examples. (Wikipedia).
What is the connection between vectors and equations of planes? Find out here! Free ebook https://bookboon.com/en/introduction-to-vectors-ebook (updated link) Test your understanding via a short quiz http://goo.gl/forms/ZTQ0pvOq1q
From playlist Introduction to Vectors
An embodiment of "Sarrus linkage 1". Two planes of two planar slider-crank mechanisms are not necessary to be perpendicular to each other. It is enough that they are not parallel.
From playlist Mechanisms
Set Theory (Part 4): Relations
Please feel free to leave comments/questions on the video and practice problems below! In this video, the notion of relation is discussed, using the interpretation of a Cartesian product as forming a grid between sets and a relation as any subset of points on this grid. This will be an im
From playlist Set Theory by Mathoma
Converting Spherical To Cartesian Coordinates
https://www.patreon.com/edmundsj If you want to see more of these videos, or would like to say thanks for this one, the best way you can do that is by becoming a patron - see the link above :). And a huge thank you to all my existing patrons - you make these videos possible. In this video
From playlist Antenna Design
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From playlist Coordinate Systems
Cartesian coordinates | Lecture 2 | Vector Calculus for Engineers
Defines Cartesian coordinates, unit vectors, the position vector and the displacement vector. Join me on Coursera: https://www.coursera.org/learn/vector-calculus-engineers Lecture notes at http://www.math.ust.hk/~machas/vector-calculus-for-engineers.pdf Subscribe to my channel: http://
From playlist Vector Calculus for Engineers
Jeremy Rouse, l-adic images of Galois for elliptic curves over Q
VaNTAGe seminar, June 22, 2021 License: CC-BY-NC-SA
From playlist Modular curves and Galois representations
Xin Li: Cartan subalgebras in C*-algebras
This talk is about the notion of Cartan subalgebras introduced by Renault, based on work of Kumjian. We explain how Cartan algebras build a bridge between dynamical systems and operator algebras, and why this notion might be interesting for the structure theory of C*-algebras as well. The
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Powered by https://www.numerise.com/ Cartesian axes & coordinates
From playlist Linear sequences & straight lines
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This video explains how to write ordered pairs and plot points on the coordinate plane. Video content created by Jenifer Bohart, William Meacham, Judy Sutor, and Donna Guhse from SCC (CC-BY 4.0)
From playlist Functions
Michel Dubois-Violette: The Weil algebra of a Hopf algebra
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebra
Stefaan Vaes - Classification of regular subalgebras of the hyperfinite II1 factor
I present a joint work with Sorin Popa and Dimitri Shlyakhtenko. We prove that under a natural condition, the regular von Neumann subalgebras B of the hyperfinite II1 factor R are completely classified (up to conjugacy by an automorphism of R) by the associated discrete measured groupoid.
From playlist Groupes, géométrie et analyse : conférence en l'honneur des 60 ans d'Alain Valette
Filip Najman, Q-curves over odd degree fields and sporadic points
VaNTAGe seminar June 29, 2021 License: CC-BY-NC-SA
From playlist Modular curves and Galois representations
Elementary Theory of Analytic Functions of One or Several Complex Variables by Henri Cartan #shorts
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From playlist Book Reviews #shorts
Oldschool Complex Analysis Book
Oldschool Complex Analysis Book This is the book on amazon: https://amzn.to/2pTP39K (note this is my affiliate link, I earn a small percentage from qualifying purchases) This is an absolute classic. The author of this book was a founding member of the Bourbaki Group and lived to be 104 y
From playlist Cool Math Stuff
Let's look at some math books:) I tried to pick books which are good and/or famous to some extent. All of these books are pretty good. Some are good for beginners and some are definitely not good for beginners. These are the books on amazon. Linear algebra by Strang https://amzn.to/3tAy
From playlist Book Reviews
What is a Coordinate Covalent Bond?
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From playlist New AP & General Chemistry Video Playlist
I give a proof of the Cartan-Hadamard theorem on non-positively curved complete Riemannian manifolds. For more details see Chapter 7 of do Carmo's "Riemannian geomety". If you find any typos or mistakes, please point them out in the comments.
From playlist Differential geometry
Using the pythagorean theorem to a rhombus
👉 Learn how to solve problems with rhombuses. A rhombus is a parallelogram such that all the sides are equal. Some of the properties of rhombuses are: all the sides are equal, each pair of opposite sides are parallel, each pair of opposite angles are equal, the diagonals bisect each other,
From playlist Properties of Rhombuses
Rafael Díaz: Deformations of N-differential graded algebras
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebra