Skip to main content
Graph
Search
fr
|
en
Login
Search
All
Categories
Concepts
Courses
Lectures
MOOCs
People
Practice
Publications
Startups
Units
Show all results for
Home
Lecture
Covariant derivatives along curves
Graph Chatbot
Related lectures (32)
Previous
Page 1 of 4
Next
Differentiating Vector Fields: Definition
Introduces differentiating vector fields along curves on manifolds with connections and the unique operator satisfying specific properties.
Connections: motivation and definition
Explores the definition of connections for smooth vector fields on manifolds.
Comparing Tangent Vectors: Parallel Transport
Explores the definition, existence, and uniqueness of parallel transport of tangent vectors on manifolds.
Acceleration and geodesics
Explains acceleration along curves and geodesics on manifolds, generalizing straight lines to spheres.
Differentiating vector fields: Why do it?
Explores the importance of differentiating vector fields and the correct methodology to achieve it, emphasizing the significance of going beyond the first order.
Connections: Axiomatic Definition
Explores connections on manifolds, emphasizing the axiomatic definition and properties of derivatives in differentiating vector fields.
Differential Forms on Manifolds
Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.
Riemannian connections
Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.
Taylor Expansions: First Order
Explores Taylor expansions of first order in optimization on manifolds.
Topology of Riemann Surfaces
Covers the topology of Riemann surfaces, focusing on orientation and orientability.
