diff --git a/src/Manifolds.jl b/src/Manifolds.jl
index 2d08d7f421..2258590533 100644
--- a/src/Manifolds.jl
+++ b/src/Manifolds.jl
@@ -220,8 +220,10 @@ using ManifoldsBase:
     ComplexNumbers,
     ComponentManifoldError,
     CompositeManifoldError,
+    CotangentSpace,
     CotangentSpaceType,
     CoTFVector,
+    CoTVector,
     DefaultBasis,
     DefaultOrthogonalBasis,
     DefaultOrthonormalBasis,
@@ -255,6 +257,7 @@ using ManifoldsBase:
     PolarInverseRetraction,
     PolarRetraction,
     PoleLadderTransport,
+    PowerBasisData,
     PowerManifold,
     PowerManifoldNested,
     PowerManifoldNestedReplacing,
@@ -728,7 +731,6 @@ export AbstractRetractionMethod,
     ODEExponentialRetraction,
     PadeRetraction,
     ProductRetraction,
-    PowerRetraction,
     SasakiRetraction
 # Inverse Retraction types
 export AbstractInverseRetractionMethod,
@@ -793,7 +795,6 @@ export ×,
     einstein_tensor,
     embed,
     embed!,
-    equiv,
     exp,
     exp!,
     flat,
@@ -806,8 +807,6 @@ export ×,
     get_embedding,
     get_orbit_action,
     get_total_space,
-    grad_euclidean_to_manifold,
-    grad_euclidean_to_manifold!,
     hat,
     hat!,
     horizontal_component,
@@ -919,7 +918,6 @@ export AbstractGroupAction,
     GroupManifold,
     GroupOperationAction,
     Identity,
-    InvariantMetric,
     LeftAction,
     LeftInvariantMetric,
     LeftSide,
diff --git a/src/groups/product_group.jl b/src/groups/product_group.jl
index 415c7dd259..571f108ed6 100644
--- a/src/groups/product_group.jl
+++ b/src/groups/product_group.jl
@@ -62,7 +62,7 @@ function Base.show(io::IO, ::MIME"text/plain", G::ProductGroup)
         io,
         "ProductGroup with $(length(base_manifold(G).manifolds)) subgroup$(length(base_manifold(G).manifolds) == 1 ? "" : "s"):",
     )
-    return _show_product_manifold_no_header(io, base_manifold(G))
+    return ManifoldsBase._show_product_manifold_no_header(io, base_manifold(G))
 end
 
 function Base.show(io::IO, G::ProductGroup)
diff --git a/src/manifolds/VectorFiber.jl b/src/manifolds/VectorFiber.jl
index bfe9a66382..410d19babb 100644
--- a/src/manifolds/VectorFiber.jl
+++ b/src/manifolds/VectorFiber.jl
@@ -1,16 +1,4 @@
 
-const CotangentSpaceAtPoint{𝔽,M} =
-    Fiber{𝔽,CotangentSpaceType,M} where {𝔽,M<:AbstractManifold{𝔽}}
-
-"""
-    CotangentSpaceAtPoint(M::AbstractManifold, p)
-
-Return an object of type [`VectorSpaceAtPoint`](@ref) representing cotangent
-space at `p`.
-"""
-function CotangentSpace(M::AbstractManifold, p)
-    return Fiber(M, CotangentSpaceType(), p)
-end
 
 """
     TensorProductType(spaces::VectorSpaceType...)
@@ -24,6 +12,10 @@ end
 
 TensorProductType(spaces::VectorSpaceType...) = TensorProductType{typeof(spaces)}(spaces)
 
+function inner(B::CotangentSpace, p, X, Y)
+    return inner(B.manifold, B.point, sharp(B.manifold, B.point, X), sharp(B.manifold, B.point, Y))
+end
+
 function Base.show(io::IO, tpt::TensorProductType)
     return print(io, "TensorProductType(", join(tpt.spaces, ", "), ")")
 end
diff --git a/test/manifolds/fiber.jl b/test/manifolds/fiber.jl
index 7582e10aa1..8bf9253d09 100644
--- a/test/manifolds/fiber.jl
+++ b/test/manifolds/fiber.jl
@@ -9,7 +9,7 @@ struct TestVectorSpaceType <: VectorSpaceType end
     @testset "tangent and cotangent space" begin
         p = [1.0, 0.0, 0.0]
         t_p = TangentSpace(M, p)
-        ct_p = CotangentSpaceAtPoint(M, p)
+        ct_p = CotangentSpace(M, p)
         t_ps = sprint(show, "text/plain", t_p)
         sp = sprint(show, "text/plain", p)
         sp = replace(sp, '\n' => "\n ")
@@ -17,10 +17,10 @@ struct TestVectorSpaceType <: VectorSpaceType end
         @test t_ps == t_ps_test
         @test base_manifold(t_p) == M
         @test base_manifold(ct_p) == M
-        @test t_p.fiber.manifold == M
-        @test ct_p.fiber.manifold == M
-        @test t_p.fiber.fiber == Manifolds.TangentFiber
-        @test ct_p.fiber.fiber == Manifolds.CotangentFiber
+        @test t_p.manifold == M
+        @test ct_p.manifold == M
+        @test t_p.fiber_type == TangentSpaceType()
+        @test ct_p.fiber_type == CotangentSpaceType()
         @test t_p.point == p
         @test ct_p.point == p
         @test injectivity_radius(t_p) == Inf
diff --git a/test/metric.jl b/test/metric.jl
index 778d4e79ee..2ec18b89f3 100644
--- a/test/metric.jl
+++ b/test/metric.jl
@@ -617,15 +617,16 @@ Manifolds.inner(::MetricManifold{ℝ,<:AbstractManifold{ℝ},Issue539Metric}, p,
         cotspace = CotangentSpace(M, p)
         cotspace2 = CotangentSpace(MM, p)
         @test coX.X ≈ X
-        @test inner(M, p, X, Y) ≈ inner(cotspace, p, coX, coY)
-        @test inner(MM, p, fX, fY) ≈ inner(cotspace, p, coX, coY)
+        X0p = zero_vector(MM, p)
+        @test inner(M, p, X, Y) ≈ inner(cotspace, X0p, coX, coY)
+        @test inner(MM, p, fX, fY) ≈ inner(cotspace, X0p, coX, coY)
 
-        @test inner(MM, p, fX, fY) ≈ inner(cotspace2, p, cofX, cofY)
+        @test inner(MM, p, fX, fY) ≈ inner(cotspace2, X0p, cofX, cofY)
         @test sharp(M, p, coX) ≈ X
 
         coMMfX = flat(MM, p, fX)
         coMMfY = flat(MM, p, fY)
-        @test inner(MM, p, fX, fY) ≈ inner(cotspace2, p, coMMfX, coMMfY)
+        @test inner(MM, p, fX, fY) ≈ inner(cotspace2, X0p, coMMfX, coMMfY)
         @test isapprox(sharp(MM, p, coMMfX).data, fX.data)
 
         @testset "Mutating flat/sharp" begin
diff --git a/test/runtests.jl b/test/runtests.jl
index c5f5f730b1..afb113cc85 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -176,7 +176,6 @@ include("utils.jl")
         include_test("manifolds/product_manifold.jl")
         include_test("manifolds/power_manifold.jl")
         include_test("manifolds/quotient_manifold.jl")
-        include_test("manifolds/fiber.jl")
         include_test("manifolds/fiber_bundle.jl")
         include_test("manifolds/vector_bundle.jl")
         include_test("manifolds/graph.jl")