Riemannian geometry
noun
                                                                                                                            
                                                            Rie·mann·ian geometry
                    
                                                                                                              
                                                                                                                                  rē-ˈmä-nē-ən-  
                                                      
                                                          
            
                                
              
          
                                                      : a non-Euclidean geometry in which straight lines are geodesics and in which the parallel postulate is replaced by the postulate that every pair of straight lines intersects                                      
                
                    
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  Merriam-Webster unabridged




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