Concept Analysis of Map Projection and Its Applications Based on Manifold Mapping Principle

Objectives and Methods: Starting from the historical origin of topological manifold and Gauss-Krüger projection, this paper firstly expounded and analyzed the principle of manifold mapping of cartographic projection and, based on which, the Earth ellipsoid or sphere was redefined from the perspective of Riemann manifold and the non-Euclidean geometric characteristics, the topological relationship with plane and their influence on map projection were analyzed. Results: Based on the principle of manifold mapping, this paper considered that the basic contradiction of map projection (i.e. the contradiction between the earth surface and the map plane) should include two aspects, namely, un-developability and un-homeomorphism, which have impacts on distortions, domains and singular points of map projection, etc. Meanwhile, the correctness and feasibility of the authors’ assertions about the principle of manifold mapping were further verified in the definition and the necessary and sufficient conditions of conformal map, etc. Conclusions： This work expanded the research idea for studying map projection from the perspective of Riemannian manifold mapping.