Symplectic manifold

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Related lectures (32)

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Riemannian metrics and gradients: Computing gradients from extensions

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

What is a smooth manifold? - Through defining functions

Explores smooth manifolds through defining functions and submanifolds, highlighting the importance of smoothness.

Tangent Spaces and Submersions

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

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.

Grassmann manifold and Retractions

Covers the Grassmann manifold and retractions on submanifolds.

Infinitesimal Deformations: One-Dimensional Maps

Explores infinitesimal deformations of one-dimensional maps, discussing common characteristics, methods, and recent results in expanding and piecewise expanding maps.

Manifolds: Charts and Compatibility

Covers manifolds, charts, compatibility, and submanifolds with smooth analytic equations.

Riemannian Geometry: Robot Motion Learning and Control

Delves into Riemannian geometry for robot motion learning and control, emphasizing geodesic synergies and the configuration space manifold.

Gradients on Riemannian submanifolds, local frames

Discusses gradients on Riemannian submanifolds and the construction of local frames.

Differentiating Vector Fields: How Not to Do It

Discusses the challenges in differentiating vector fields on submanifolds and the importance of choosing the right method.