Curvature of Riemannian manifolds

Curvature of a Riemannian Manifold | Riemannian Geometry

In this lecture, we define the exponential mapping, the Riemannian curvature tensor, Ricci curvature tensor, and scalar curvature. The focus is on an intuitive explanation of the curvature tensors. The curvature tensor of a Riemannian metric is a very large stumbling block for many student

From playlist All Videos

The Curvature of a Circle

The Curvature of a Circle

From playlist Calculus 3

Connections part 5: Riemannian Curvature Tensor and Faraday Tensor

This video was hacked together. Apologies.

From playlist Connections, Curvature and Covariant Derivatives

Lecture 15: Isometries, Rigidity, and Curvature

CS 468: Differential Geometry for Computer Science

From playlist Stanford: Differential Geometry for Computer Science (CosmoLearning Computer Science)

Curvature and Radius of Curvature for a function of x.

This video explains how to determine curvature using short cut formula for a function of x.

From playlist Vector Valued Functions

Connections part 4: Two incarnations of curvature and the de Rham complex

From playlist Connections, Curvature and Covariant Derivatives

Multivariable Calculus | Curvature

We define the notion of the curvature of a vector valued function, prove an equivalent definition, and find the curvature of a circle of radius a. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Multivariable Calculus

What is Curvature? Calculus 3

What is Curvature? Calculus 3

From playlist Calculus 3

The Cartan-Hadamard theorem

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

Jialong Deng - Enlargeable Length-structures and Scalar Curvatures

38th Annual Geometric Topology Workshop (Online), June 15-17, 2021 Jialong Deng, University of Goettingen Title: Enlargeable Length-structures and Scalar Curvatures Abstract: We define enlargeable length-structures on closed topological manifolds and then show that the connected sum of a

From playlist 38th Annual Geometric Topology Workshop (Online), June 15-17, 2021

Emanuel Milman: Functional Inequalities on sub-Riemannian manifolds via QCD

We are interested in obtaining Poincar ́e and log-Sobolev inequalities on domains in sub-Riemannian manifolds (equipped with their natural sub-Riemannian metric and volume measure). It is well-known that strictly sub-Riemannian manifolds do not satisfy any type of Curvature-Dimension condi

From playlist Workshop: High dimensional measures: geometric and probabilistic aspects

Curvature and Radius of Curvature for 2D Vector Function

This video explains how to determine curvature using short cut formula for a vector function in 2D.

From playlist Vector Valued Functions

Entropy of manifolds and of their fundamental group - Gerard Besson

Workshop on Geometric Functionals: Analysis and Applications Topic: Entropy of manifolds and of their fundamental group Speaker: Gerard Besson Affiliation: Université de Grenoble Date: March 7, 2019 For more video please visit http://video.ias.edu

From playlist Mathematics

C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 1 (version temporaire)

We introduce various notions of convergence of Riemannian manifolds and metric spaces. We then survey results and open questions concerning the limits of sequences of Riemannian manifolds with uniform lower bounds on their scalar curvature. We close the course by presenting methods and the

From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics

Mokshay Madiman : Minicourse on information-theoretic geometry of metric measure

Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the August 28, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematician

From playlist Geometry

D. Prandri - Weyl law for singular Riemannian manifolds

In this talk we present recent results on the asymptotic growth of eigenvalues of the Laplace-Beltrami operator on singular Riemannian manifolds, where all geometrical invariants appearing in classical spectral asymptotics are unbounded, and the total volume can be infinite. Under suitable

From playlist Journées Sous-Riemanniennes 2018

Poincare Conjecture and Ricci Flow | A Million Dollar Problem in Topology

How do we use Riemannian Geometry and Surgery Theory to crack a million-dollar problem in topology? Ricci flow, that's how. In this video, we tackle the only Millennium Prize Problem that's been solved so far, and find the deep mathematics uncovered in the process. --- Official Problem St

From playlist Famous Unsolved Problems

What is General Relativity? Lesson 68: The Einstein Tensor

What is General Relativity? Lesson 68: The Einstein Tensor The Einstein tensor defined! Using the Ricci tensor and the curvature scalar we can calculate the curvature scalar of a slice of a manifold using the Einstein tensor. Please consider supporting this channel via Patreon: https:/

From playlist What is General Relativity?

Jan Maas : Gradient flows and Ricci cuevature in discrete and quantum probability

Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the August 28, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent

From playlist Geometry