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We introduce a method in differential geometry to study the derivativeoperators of Siegel modular forms. By determining the coefficients of theinvariant Levi-Civita connection on a Siegel upper half plane, and further bycalculating the expressions of the differential forms under this connection, weget a non-holomorphic derivative operator of the Siegel modular forms. In orderto get a holomorphic derivative operator, we introduce a weaker notion, calledmodular connection, on the Siegel upper half plane than a connection indifferential geometry. Then we show that on a Siegel upper half plane thereexists at most one holomorphic modular connection in some sense, and get apossible holomorphic derivative operator of Siegel modular forms.

Derivations of Siegel Modular Forms from Connections