2025-05-15 First post This is a first post. Testing math g(∇XBY,Z)=g(∇XY,Z)−12c(X,Y,Z)g(\nabla_X^BY,Z) = g(\nabla_XY,Z) - \frac{1}{2} c(X,Y,Z)g(∇XBY,Z)=g(∇XY,Z)−21c(X,Y,Z) where c(X,Y,Z)=g(TB(X,Y),Z)=JdF(X,Y,Z)=dF(JX,JY,JZ)c(X,Y,Z) = g(T^B(X,Y),Z) = JdF(X,Y,Z) = dF(JX,JY,JZ)c(X,Y,Z)=g(TB(X,Y),Z)=JdF(X,Y,Z)=dF(JX,JY,JZ).