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math.DG2023
Geometry in global coordinates in mechanics and optimal transport
Du Nguyen
For a manifold embedded in an inner product space, we express geometric quantities such as {\it Hamilton vector fields, affine and Levi-Civita connections, curvature} in global coo…
math.DG2021
Riemannian Geometry with differentiable ambient space and metric operator
Du Nguyen
We show Riemannian geometry could be studied by identifying the tangent bundle of a Riemannian manifold with a subbundle of the trivial bundle $\mathcal{M} \times \ma…