Update Readme II.

README.md

@@ -3,19 +3,33 @@
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-
 Basic interface for manifolds in Julia.
 
 The project [`Manifolds.jl`](https://github.com/JuliaManifolds/Manifolds.jl)
 is based on this interface and provides a variety of manifolds.
 
+## `DecoratorManifold`
+
+The decorator manifold enhances a manifold by certain, in most cases implicitly
+assumed to have a standard case, properties, see for example the `EmbeddedManifold`.
+The decorator acts semi transparently, i.e. `:transparent` for all functions not affected by that
+decorator and `:intransparent` otherwise. Another possibility is, that the decorator just
+passes to `:parent` in order to fill default values.
+
 ## `DefaultManifold`
 
 This interface includes a simple `DefaultManifold`, which is a reduced version
 of the [`Euclidean`](https://github.com/JuliaManifolds/Manifolds.jl/blob/master/src/Euclidean.jl)
 manifold from [`Manifolds.jl`](https://github.com/JuliaManifolds/Manifolds.jl),
 such that the interface functions can be tested.
 
+## Embedded Manifold
+
+The embedded manifold models the embedding of a manifold into another manifold.
+This way a manifold can benefit from existing implementations.
+One example is the `TransparentIsometricEmbeddingType` where a manifold uses the metric,
+`inner`, from its embedding.
+
 ## `ArrayManifold`
 
 The `ArrayManifold` further illustrates how one can also used types to