$\displaystyle \nabla_{X}Y:=D_{X}Y + (1/2).(XxY)$

is this a riemannian connection?

somebody please try to solve this.i am implementing the 6 properties given at kuhnel's differential geometry book,in the book it was written there is problem with the 6th property but i think there is no problem with that propertie can anybody check that?