Submanifolds — Topic Summaries
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Manifolds 19 | Tangent Space for Submanifolds
Tangent spaces for submanifolds in Euclidean space are built directly from derivatives of local parameterizations, turning the geometry of a curved...
Manifolds 34 | Examples for Riemannian Manifolds
Riemannian manifolds gain their geometry from a smoothly varying inner product on each tangent space, and the most practical way to build that...
Manifolds 19 | Tangent Space for Submanifolds [dark version]
Tangent spaces for submanifolds in 9n are built by taking the range of the differential of a local parameterization, turning the geometry of a...
Manifolds 13 | Examples of Smooth Manifolds [dark version]
A concrete check of the transition maps shows why the n-dimensional sphere carries a C∞ smooth structure: every overlap map between its standard...