Riemannian metrics and gradients: Computing gradients from extensions

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (32)

Page 3 of 4

Shells I: Mechanics of Slender Structures

Covers linear and membrane theories of pressure vessels, differential geometry of surfaces, and the reduction of dimensionality from 3D to 2D.

Tangent Spaces and Submersions

Covers tangent spaces and submersions in differential geometry, emphasizing vector spaces and differentiable structures.

Tangent vectors without embedding space: Revisiting the embedded case

Explores defining tangent vectors without an embedding space, focusing on creating tangent spaces at every point of a manifold through equivalence classes of curves.

Riemannian Hessians: Definition and Example

Covers the definition and computation of Riemannian Hessians on manifolds.

Differentiating vector fields along curves: Examples and finite differences

Covers the differentiation of vector fields along curves with examples and finite differences.

Conformal Symmetries in Euclidean and AdS Spaces

Explores conformal symmetries in Euclidean and AdS spaces, isometries, induced metric, Poincaré coordinates, and boundary structure.

Smooth maps on manifolds and differentials

Covers smooth maps on manifolds, defining functions, tangent spaces, and differentials.

From embedded to general manifolds: upgrading our foundations

Explores the transition from embedded to general manifolds, upgrading foundational concepts and discussing mathematical reasons for both approaches.

Curves with Poritsky Property and Liouville Nets

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

Riemannian Hessians: Connections and Symmetry

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