The comparative analysis of existing definitions of the subject of geography on the basis of theoretical and mathematical statements leads to the conclusion that the unique subject of geographical research is the geographical environment, which differently takes into account in different system models. For this reason, the geography is developed as a complementary cognitive system that is alternative to other sciences on geographical cover of the Earth. Knowledge of geography complements the knowledge of other sciences to display in the laws the unity of the different systems and their environment. To formalize this rule, the mathematical procedures of the tangent bundle of the manifold relations of the environmental characteristics are used. It leads to the formulation of extreme principle of interaction of the object with the environment and creates episystem models of the relationship between spatial objects.