Concept

Christoffel symbols

Related lectures (15)

Covariant Derivatives and Christoffel Symbols

Covers accelerated and inertial coordinate systems, Jacobian, volume elements, covariant derivatives, Christoffel symbols, Lorentz case, and metric tensor properties.

Christoffel Symbols and Gravity Before Einstein

Introduces Christoffel symbols and gravity concepts before Einstein, discussing mathematical tensors and the Nobel Prize in Physics.

Tensor Analysis: Coordinate Systems

Covers tensor analysis for arbitrary coordinate systems and introduces Christoffel symbols.

Linear Shell Theory: Equilibrium Equations

Covers the dimensional reduction of strain energy from 3D to 2D and linear shell theory equilibrium equations.

Tensor Properties

Covers the properties of tensors and their applications in various fields.

Exponential Map and Curvature Tensor

Covers the exponential map, covariant derivatives, connection coefficients, and Riemann curvature tensor.

Shells I

Covers linear pressure vessels, thin shells, and critical buckling pressure, emphasizing the dimensional reduction from 3D to 2D.

Riemannian connections: Proof sketch

Presents the fundamental theorem of Riemannian geometry and demonstrates the uniqueness of the Riemannian connection.

Riemannian metrics and gradients: Computing gradients from extensions

Explores computing gradients on Riemannian manifolds through extensions and retractions, emphasizing orthogonal projectors and smooth extensions.

Dispositionalism & Laws of Nature

Delves into dispositionalism, laws of nature, Humean metaphysics, and Super-Humeanism in explaining fundamental physics.

Vorticity Equation: Levi-Civita Symbol

Explores the vorticity equation, Levi-Civita symbol, stress tensor, and helicity derivation.

Riemannian Hessians: Connections and Symmetry

Covers connections on manifolds, symmetric connections, Lie brackets, and compatibility with the metric in Riemannian geometry.

Riemannian metrics and gradients: Riemannian gradients

Explains Riemannian submanifolds, metrics, and gradients computation on manifolds.

Gradient and Hessian of Pullback

Explores the connection between Riemannian and Euclidean gradients and Hessians at critical points.

Shells I: Mechanics of Slender Structure

Covers thin pressure vessels, differential geometry of surfaces, and plate buckling theories.