diff --git a/src/manifolds/ConnectionManifold.jl b/src/manifolds/ConnectionManifold.jl
index 38dd212a28..bde024879e 100644
--- a/src/manifolds/ConnectionManifold.jl
+++ b/src/manifolds/ConnectionManifold.jl
@@ -106,15 +106,23 @@ function christoffel_symbols_second_jacobian(
     M::AbstractManifold,
     p,
     B::AbstractBasis;
-    backend::AbstractDiffBackend=diff_backend(),
+    backend::AbstractDiffBackend=default_differential_backend(),
 )
-    n = size(p, 1)
+    d = manifold_dimension(M)
     ∂Γ = reshape(
-        _jacobian(q -> christoffel_symbols_second(M, q, B; backend=backend), p, backend),
-        n,
-        n,
-        n,
-        n,
+        _jacobian(
+            c -> christoffel_symbols_second(
+                M,
+                exp(M, p, get_vector(M, p, c, B)),
+                B;
+                backend=backend
+            ),
+            p,
+            backend),
+        d,
+        d,
+        d,
+        d,
     )
     return ∂Γ
 end
@@ -236,7 +244,7 @@ function riemann_tensor(
     M::AbstractManifold,
     p,
     B::AbstractBasis;
-    backend::AbstractDiffBackend=diff_backend(),
+    backend::AbstractDiffBackend=default_differential_backend(),
 )
     n = size(p, 1)
     Γ = christoffel_symbols_second(M, p, B; backend=backend)