Tag Archives: projective structure

Geometric structures on 1-manifolds

A geometric structure on a manifold is an atlas of charts with values in some kind of “model space”, and transformation functions taken from some pseudogroup of transformations on the model space. If is the model space, and is the … Continue reading

Posted in Lie groups | Tagged , , , , , , , , , , | 1 Comment

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 , , , , , , | 5 Comments