section_path: Contemporary geometry/Differential geometry
section_name: Differential geometry
paragraph_text: Differential geometry
  
  Differential geometry uses techniques of calculus and linear algebra to study problems in geometry. It has applications in physics, econometrics, and bioinformatics, among others.
  
  In particular, differential geometry is of importance to mathematical physics due to Albert Einstein 's general relativity postulation that the universe is curved. Differential geometry can either be intrinsic (meaning that the spaces it considers are smooth manifolds whose geometric structure is governed by a Riemannian metric, which determines how distances are measured near each point) or extrinsic (where the object under study is a part of some ambient flat Euclidean space).