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Quick Facts

Medium Of InstructionsMode Of LearningMode Of Delivery
EnglishSelf StudyVideo and Text Based

Courses and Certificate Fees

Fees InformationsCertificate AvailabilityCertificate Providing Authority
INR 1000yesIIT Kanpur

The Syllabus

  • Hyperbolic Geometry
  • Models of Hyperbolic space
  • Upper half plane and Unit Disc with Poincaré metric
  • Hyperbolic Inner Product, Geodesics 
  • Isometry Groups 
  • Classification of Isometries
  • Area of Triangles 
  • Trignometric Identities.

  • Properly discontinous action
  • Cocompact action
  • Fuchsian Group
  • Covering Space
  • Fundamental Region
  • Tesellation
  • Algebraic properties of Fuchsian Group
  • Hyperbolic surfaces
  • Poincaré’s Theorem (Statement Only) Closed curves and geodesics on Hyperbolic Surfaces

  • Slim and Thin triangles
  • Hyperbolic metric space
  • Exponential Divergence
  • Stability of Quasi-geodesics 
  • Hyperbolic groups and its properties

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