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Just a bit of docs before I got confused again
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src/FiberBundle.jl

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"""
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FiberBundle{𝔽,TVS<:FiberType,TM<:AbstractManifold{𝔽},TVT<:FiberBundleProductVectorTransport} <: AbstractManifold{𝔽}
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Fiber bundle on a [`AbstractManifold`](https://juliamanifolds.github.io/ManifoldsBase.jl/stable/types.html#ManifoldsBase.AbstractManifold) `M`
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of type [`FiberType`](@ref).
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Fiber bundle on a [`AbstractManifold`](@ref) `M` of type [`FiberType`](@ref).
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Examples include vector bundles, principal bundles or unit tangent bundles, see also [📖 Fiber Bundle](https://en.wikipedia.org/wiki/Fiber_bundle).
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# Fields
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* `manifold` – the [`AbstractManifold`](@ref) manifold the Fiber bundle is defined on
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* `type` – representing the type of fiber we use.
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# Constructor
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FiberBundle(M::AbstractManifold, type::FiberType)
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vector_transport::TVT
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end
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vector_bundle_transport(::FiberType, M::AbstractManifold) = ParallelTransport()
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function FiberBundle(
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fiber::TVS,
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M::TM,
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return FiberBundle(fiber, M, vtbm)
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end
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vector_bundle_transport(::FiberType, M::AbstractManifold) = ParallelTransport()
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struct FiberBundleBasisData{BBasis<:CachedBasis,TBasis<:CachedBasis}
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base_basis::BBasis
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fiber_basis::TBasis

src/VectorBundle.jl

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"""
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VectorBundle{𝔽,TVS,TM,TVT}
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VectorBundle{𝔽,TVS,TM,VTV} = = FiberBundle{𝔽, VectorSpaceFiberType{TVS},TM,TVT}
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Alias for [`FiberBundle`](@ref) when fiber type is a `TVS` of type
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[`VectorSpaceType`](https://juliamanifolds.github.io/ManifoldsBase.jl/stable/bases.html#ManifoldsBase.VectorSpaceType).
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[`VectorSpaceType`](@ref).
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`VectorSpaceFiberType` is used to encode vector spaces as fiber types.
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"""

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