  We introduce a method in differential geometry to study the derivative
operators of Siegel modular forms. By determining the coefficients of the
invariant Levi-Civita connection on a Siegel upper half plane, and further by
calculating the expressions of the differential forms under this connection, we
get a non-holomorphic derivative operator of the Siegel modular forms. In order
to get a holomorphic derivative operator, we introduce a weaker notion, called
modular connection, on the Siegel upper half plane than a connection in
differential geometry. Then we show that on a Siegel upper half plane there
exists at most one holomorphic modular connection in some sense, and get a
possible holomorphic derivative operator of Siegel modular forms.
