Riemannian metrics and gradients: Computing gradients from extensions

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Covers Newton's method on Riemannian manifolds, focusing on second-order optimality conditions and quadratic convergence.

Tangent spaces to submanifolds

Introduces tangent spaces to submanifolds and their properties in optimization on manifolds.

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Gradients on Riemannian submanifolds, local frames

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

Riemannian metrics and gradients: Riemannian gradients

Explains Riemannian submanifolds, metrics, and gradients computation on manifolds.

Dynamics of Steady Euler Flows: New Results

Explores the dynamics of steady Euler flows on Riemannian manifolds, covering ideal fluids, Euler equations, Eulerisable flows, and obstructions to exhibiting plugs.

Optimality Conditions: First Order

Covers optimality conditions in optimization on manifolds, focusing on global and local minimum points.

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.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Optimization on Manifolds: Context and Applications

Introduces optimization on manifolds, covering classical and modern techniques in the field.