Let E be a vector bundle over M and ∇, a connection, I can define e∇X, it verifies:
e∇X(f.s)=(eXf).e∇X(s)
where s is a section, f a smooth function over M and X a vector field over M. I define:
˜R∇(X,Y)=et∇Xet∇Ye−t∇Xe−t∇Ye−t2∇[X,Y]
It verifies:
˜R∇(X,Y)=1+t2R∇(X,Y)+o(t2)
where R∇ is the curvature of ∇. Is it bound to the holonomy of the connection ∇?