Some Nonlinear Problems in Riemannian Geometry.pdf

Some Nonlinear Problems in Riemannian Geometry

Thierry Aubin

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Some Nonlinear Problems in Riemannian Geometry Some Nonlinear Problems in Riemannian Geometry Springer. Contents Chapter 1 Riemannian Geometry §1. Introduction to Differential Geometry 1 1.1. Tangent Space 2 1.2. Connection 3 1.3. Curvature 3 §2. Riemannian Manifold 4 2.1. Metric Space 5 2.2. Riemannian Connection 6 2.3. Sectional Curvature. Ricci Tensor. Scalar Curvature 6 2.4. Parallel Displacement. Geodesic 8 §3. Exponential Mapping

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9783540607526 ISBN
Some Nonlinear Problems in Riemannian Geometry.pdf

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general theory of neural networks in the setting of Riemannian geometry. From this perspective ... avoid problems with long term dependencies. ... layers successively warp the coordinate representation of the data manifold with nonlinear trans- ... some resemblance to group closure, with group operation vector addition.

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