A new view of combinatorial maps by Smarandache's notion

On a geometrical view, the conception of map geometries are introduced, which is a nice model of the Smarandache geometries, also new kind of and more general intrinsic geometry of surface. Results convinced one that map geometries are Smarandache geometries and their enumertion are obtained. Open problems related combinatorial maps with the Riemann geometry and Smarandache geometries are also presented in this paper.