sentences:  In a geodesic polar system, the Gaussian curvature formula_2 can be expressed as 
  
  In addition K is constant and fulfills the following differential equation 
  
  Since formula_20 and formula_6 have the same constant Gaussian curvature, then they are locally isometric (Minding's Theorem).That means that formula_33 is a local isometry between formula_20 and formula_6.Furthermore, from the Hadamard's theorem it follows that formula_33 is also a covering map.