Tag Archives: Schwarzian derivative

Schwarz-Christoffel transformations, Schwarzian derivatives, and Schwarz’s minimal surface

Hermann Amandus Schwarz (1843-1921) was a student of Kummer and Weierstrass, and made many significant contributions to geometry, especially to the fields of minimal surfaces and complex analysis. His mathematical creations are both highly abstract and flexible, and at the … Continue reading

Posted in Complex analysis, Euclidean Geometry, Surfaces | Tagged , , , , , , , | 4 Comments

Cubic forms in differential geometry

Quadratic forms (i.e. homogeneous polynomials of degree two) are fundamental mathematical objects. For the ancient Greeks, quadratic forms manifested in the geometry of conic sections, and in Pythagoras’ theorem. Riemann recognized the importance of studying abstract smooth manifolds equipped with … Continue reading

Posted in Symplectic geometry | Tagged , , , , , , | 3 Comments