Riemannian geometry | Connection (mathematics)

Levi-Civita connection

In Riemannian or pseudo Riemannian geometry (in particular the Lorentzian geometry of general relativity), the Levi-Civita connection is the unique affine connection on the tangent bundle of a manifold (i.e. affine connection) that preserves the (pseudo-)Riemannian metric and is torsion-free. The fundamental theorem of Riemannian geometry states that there is a unique connection which satisfies these properties. In the theory of Riemannian and pseudo-Riemannian manifolds the term covariant derivative is often used for the Levi-Civita connection. The components (structure coefficients) of this connection with respect to a system of local coordinates are called Christoffel symbols. (Wikipedia).

Levi-Civita connection
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levitron

This levitron manufactured by my friend İzzet Özgöçmen. We enjoyed playing with it.

From playlist Izzet Özgöçmen

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The Pronoun Ci in Italian

Since we just learn the pronoun ne, let's learn another one: ci. This has a lot of uses, as ci locativo, ci argomentale, and more. Let's learn how to use it! Script by Patrizia Farina, Professor of Italian at Western Connecticut State University and Purchase College. Watch the whole Ital

From playlist Italian

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An Oxford Mathematics Graduate Supervision - Geometry and Physics in 7 Dimensions

So how do supervisor & graduate student work together? What happens in a graduate supervision? To find out, we filmed a supervision. Introducing Professor Jason Lotay & graduate student Izar Alonso Lorenzo as they discuss geometry in seven dimensions related to special holonomy, gauge the

From playlist Oxford Mathematics Student Tutorials and Graduate Supervisions

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AWESOME antigravity electromagnetic levitator (explaining simply)

Physics levitron (science experiments)

From playlist ELECTROMAGNETISM

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Levi-Civita and Kronecker: A Remarkable Relationship | Deep Dive Maths

There is a remarkable relationship between the product of two Levi-Civita symbols and the determinant of a matrix with the Kronecker delta as elements. After defining the Levi-Civita symbol and the Kronecker delta, I show how to derive this relationship using permutation matrices and the

From playlist Deep Dive Maths

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Kronecker delta and Levi-Civita symbol | Lecture 7 | Vector Calculus for Engineers

Definition of the Kronecker delta and the Levi-Civita symbol (sometimes called the permutation symbol or Levi-Civita tensor). The relationship between the Kronecker delta and the Levi-Civita symbol is discussed. Join me on Coursera: https://www.coursera.org/learn/vector-calculus-engin

From playlist Vector Calculus for Engineers

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Vector Triple Product | Lecture 10 | Vector Calculus for Engineers

The vector triple product identity is proved using the Levi-Civita symbol and the Einstein summation convention. 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

From playlist Vector Calculus for Engineers

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Divergence of the cross product of two vectors (proof) | Lecture 22 | Vector Calculus for Engineers

An example of how to prove a vector calculus identity using the Levi-Civita symbol and the Kronecker delta. 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 ch

From playlist Vector Calculus for Engineers

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Stardust Discovery, and 2 Planetary Conjunctions

SciShow Space shares the latest developments from around the universe, including news about the first material ever collected from outside the solar system, and a backyard astronomers’ guide to two upcoming planetary conjunctions. Hosted by: Reid Reimers ---------- Like SciShow? Want to h

From playlist SciShow Space

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04: D´Alembert´s principle part 2

Jacob Linder: Lecture 2, 11.01.2012, Klassisk Mekanikk (TFY 4345) v2012 NTNU A full textbook covering the material in the lectures in detail can be downloaded for free here: http://bookboon.com/en/introduction-to-lagrangian-hamiltonian-mechanics-ebook

From playlist NTNU: TFY 4345 - Classical Mechanics | CosmoLearning Physics

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Levitation magnet on a stirrer (Foucault currents)!!!

In this video i demonstrate levitation magnet on aluminum plate with stirrer. Enjoy!

From playlist ELECTROMAGNETISM

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Lagrange Bicentenary - Cédric Villani's conference

From the stability of the Solar system to the stability of plasmas

From playlist Bicentenaire Joseph-Louis Lagrange

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Vector Identities | Lecture 8 | Vector Calculus for Engineers

Four vector identities are presented: (1) Scalar triple product; (2) Vector triple product; (3) Scalar quadruple product; (4) Vector quadruple product. The tools required to prove them are discussed. Join me on Coursera: https://www.coursera.org/learn/vector-calculus-engineers Lecture n

From playlist Vector Calculus for Engineers

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Solving the Mysteries of Saturn

This week on SciShow Space News, Cassini visited Saturn’s moon Dione for the last time, and two little shepherd moons may have helped form some of Saturn’s rings. ---------- Dooblydoo thanks go to the following Patreon supporters -- we couldn't make SciShow without them! Shout out to Justi

From playlist Space News - SciShow Space

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Lagrange Interpolation

A basic introduction to Lagrange Interpolation. Chapters 0:00 Introduction 01:07 Lagrange Polynomials 03:58 The Lagrange Interpolation formula 05:10 The Resulting Polynomials The product links below are Amazon affiliate links. If you buy certain products on Amazon soon after clicking th

From playlist Interpolation

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Tensor Calculus Lecture 7c: The Levi-Civita Tensors

This course will eventually continue on Patreon at http://bit.ly/PavelPatreon Textbook: http://bit.ly/ITCYTNew Errata: http://bit.ly/ITAErrata McConnell's classic: http://bit.ly/MCTensors Table of Contents of http://bit.ly/ITCYTNew Rules of the Game Coordinate Systems and the Role of Te

From playlist Introduction to Tensor Calculus

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49: April Hamilton Jacobi theory - Part 1

Jacob Linder: 12.04.2012, Classical Mechanics (TFY4345), v2012 NTNU A full textbook covering the material in the lectures in detail can be downloaded for free here: http://bookboon.com/en/introduction-to-lagrangian-hamiltonian-mechanics-ebook

From playlist NTNU: TFY 4345 - Classical Mechanics | CosmoLearning Physics

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Can you prove the Why equation? Part 2

This amazingly simple equation can be proved in just two short lines. Watch the video to learn how.

From playlist Summer of Math Exposition Youtube Videos

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AWESOME Antigravity experiment! Levitron!

I show an interesting commercially available toy that is the highest magnetic levitation device we've seen so far.

From playlist MAGNETISM

Related pages

Tangent bundle | Covariant derivative | Fundamental theorem of Riemannian geometry | Lie bracket of vector fields | Albert Einstein | Holonomy | Unit sphere | Metric connection | Isomorphism | Constant curvature | Elwin Bruno Christoffel | Curve | L. E. J. Brouwer | Riemann curvature tensor | Pullback bundle | Hypersurface | Jan Arnoldus Schouten | Gregorio Ricci-Curbastro | Christoffel symbols | Polar coordinate system | Riemannian manifold | Section (fiber bundle) | Euclidean space | Manifold | Tullio Levi-Civita | Metric tensor | Hermann Weyl | Orthogonal group | Parallel transport | Q.E.D. | Euclidean distance | Euclidean vector | Affine connection | Pseudo-Riemannian manifold | Pullback (differential geometry) | Vector field