A note on second-order Taylor expansion on Riemannian manifolds
FrnkNlsn · x · 2026-07-28
A note on the second-order Taylor expansion of a smooth function on a Riemannian manifold.
- The Riemannian gradient depends on the metric g.
- The Riemannian Hessian depends on the affine connection ∇.
- The formula is useful for optimization on Riemannian manifolds, with the slide also defining geodesics, gradients, and Hessians in this setting.
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