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Angular momentum, convex Polyhedra and Algebraic Geometry

Published online by Cambridge University Press:  20 January 2009

M. F. Atiyah
M. F. Atiyah
Affiliation:
Mathematical Institute, 24-29 St. Giles, Oxford OX1 3LB, England
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The three families of classical groups of linear transformations (complex, orthogonal, symplectic) give rise to the three great branches of differential geometry (complex analytic, Riemannian and symplectic). Complex analytic geometry derives most of its interest from complex algebraic geometry, while symplectic geometry provides the general framework for Hamiltonian mechanics.

These three classical groups “intersect” in the unitary group and the three branches of differential geometry correspondingly “intersect” in Kähler geometry, which includes the study of algebraic varieties in projective space. This is the basic reason why Hodge was successful in applying Riemannian methods to algebraic geometry in his theory of harmonic forms.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 26 , Issue 2 , June 1983 , pp. 121 - 133
Copyright
Copyright © Edinburgh Mathematical Society 1983

References

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