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Tag Archives: Differential Geometry
Donaldson Turns 60
“Donaldson has opened up an entirely new area; unexpected and mysterious phenomena about the geometry of 4dimensions have been discovered. Moreover, the methods are new and extremely subtle, using difficult nonlinear partial differential equations. On the other hand, this theory … Continue reading
Posted in Algebraic Geometry, Math, Topology
Tagged Differential Geometry, Math, Topology
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What is a Manifold? (5/6)
In our last post, we invented a new geometry by rescaling the inner product of the usual Euclidean plane. This modification did not change any of the angles in our geometry, in the sense that if two curves intersected in a particular Euclidean … Continue reading
What is a Manifold? (4/6)
After our luxurious treatment of 1d manifolds, we turn to 2d manifolds. My story of surfaces starts in a beautifully weird morning when I got up to realize that life in the usual Euclidean plane had changed dramatically. Vectors had shortened, areas … Continue reading