We consider 2-dimensional semialgebraic topological manifolds from the differentialgeometric point of view. Curvatures at singularities are defined and a Gauss-Bonnet formula holds. Moreover, Aleksandrov's axioms for an intrinsic geometry of surfaces are fulfilled.
@article{urn:eudml:doc:44250, title = {Inner metric properties of 2-dimensional semi-algebraic sets.}, journal = {Revista Matem\'atica de la Universidad Complutense de Madrid}, volume = {10}, year = {1997}, pages = {51-78}, zbl = {0920.14030}, mrnumber = {MR1485291}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44250} }
Bröcker, L.; Kuppe, M.; Scheufler, W. Inner metric properties of 2-dimensional semi-algebraic sets.. Revista Matemática de la Universidad Complutense de Madrid, Tome 10 (1997) pp. 51-78. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44250/