Retractions: second order

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

Covers optimization on manifolds, focusing on smooth manifolds and functions, and the process of gradient descent.

Explores the definition of connections for smooth vector fields on manifolds.

Covers manifolds, topology, smooth maps, and tangent vectors in detail.

Covers smooth maps, vector fields, and retractions on manifolds, emphasizing the importance of smoothly varying curves.

Introduces Manopt, a toolbox for optimization on manifolds, focusing on solving optimization problems on smooth manifolds using the Matlab version.

Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.

Explores covariant derivatives along curves and second-order optimality conditions in vector fields and manifolds.

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

Explores geodesics in the Wasserstein space, emphasizing constant speed geodesics and their properties.

Covers the definition of retraction, open submanifolds, local defining functions, tangent spaces, and Riemannian metrics.

Explores non-analytic smooth functions, their properties, and applications in differential geometry and partitioning unity.

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