Dos estructuras: = ( , ∇ , ) μ=(M,∇,g) y ˉ = ( , ∇ ˉ , ) μ ˉ ​ =(M, ∇ ˉ ,g) tales que: { ( ∇ ) ( , ) = ( , , ) , ( , , ) ∈ ∞ ( ) ( , ) = ∇ − ∇ − [ , ] { (∇ U ​ g)(V,W)=A(U,V,W),A(U,V,W)∈C ∞ (M) S(U,V)=∇ U ​ V−∇ V ​ U−[U,V] ​ (1) { ( ∇ ˉ ) ( , ) = 0 ˉ ( , ) = ∇ ˉ − ∇ ˉ − [ , ] , , , ∈ ( ) { ( ∇ ˉ U ​ g)(V,W)=0 S ˉ (U,V)= ∇ ˉ U ​ V− ∇ ˉ V ​ U−[U,V],U,V,W∈χ(M) ​ son H-equivalentes, si existe una aplicación : ( ) × ( ) → ( ) H:χ(M)×χ(M)→χ(M), tal que: ∇ ˉ = ∇ + ( , ) . ∇ ˉ U ​ V=∇ U ​ V+H(U,V). (2)