Not all the geometrical structures are "equal". It would seem that the riemannian and complex structures, with their contacts with other fields of mathematics and with their richness in results, should occupy a central position in differential geometry. A unifying idea is the notion of a G-structure, which is the modern version of an equivalence problem first emphasized and exploited in its various special cases by Elie Cartan.
Shiing-Shen ChernRelated topics
central complex differential equal equivalence geometry idea mathematics position problem should unifying version FieldsRelated quotes
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