Creating a manifold and project it onto a higher dimension in julia

Question

I'm very new to topology. Suppose I want to create a 1/2/3 dim manifold, and project it onto a 10 dimensional space. How should I do that? I went through the website https://juliamanifolds.github.io/Manifolds.jl/v0.1/interface.html#

And my current code is like

using ManifoldsBase, LinearAlgebra, Test
import ManifoldsBase: check_point, check_vector, manifold_dimension, exp!, inner, representation_size, get_embedding
import Base: show

"""
    ScaledSphere{N} <: AbstractDecoratorManifold{ℝ}

Define an `N`-sphere of radius `r`. Construct by `ScaledSphere(radius,n)`.
"""
struct ScaledSphere{N} <: AbstractDecoratorManifold{ManifoldsBase.ℝ} where {N}
    radius::Float64
end
ScaledSphere(radius, n) = ScaledSphere{n}(radius)
Base.show(io::IO, M::ScaledSphere{n}) where {n} = print(io, "ScaledSphere($(M.radius),$n)")
S = ScaledSphere(1.5, 2)

I can only find how to project a point onto a tangent vector, but what about project a point/circle/sphere onto the 10-dimensional space?