Lie bracket of vector fields

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Page 2 of 4

Covers Riemannian connections, emphasizing their properties and significance in geometry.

Explores gradient in scalar fields, directional derivatives, and level sets.

Explores the definition, existence, and uniqueness of parallel transport of tangent vectors on manifolds.

Explores the dynamics of singular Riemann surface foliations, focusing on vector fields, linear parts, and coordinate changes.

Explores how sources and sinks affect the divergence of vector fields.

Explores the geometric interpretation of line integrals in altimetric profiles of cycling stages.

Explores the Gauss theorem in R^n+1, covering regular domains, vector fields, surface integrals, and volume calculations.

Introduces retractions and vector fields on manifolds, providing examples and discussing smoothness and extension properties.

Covers the concept of local frames, their construction, and limitations.

Explores the divergence theorem and corollaries related to Green identities in the plane, demonstrating their application through examples.