Model geometries in the space of Riemannian structures and Hamilton's flow

Details Model geometries in the space of Riemannian structures and Hamilton's flow Model geometries in the space of Riemannian structures and Hamilton's flow

May 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988cqgra...5..659c&link_type=abstract

Classical and Quantum Gravity (ISSN 0264-9381), vol. 5, May 1, 1988, p. 659-693.

Computer Science

14

Hamiltonian Functions, Riemann Manifold, Space-Time Functions, Cosmology, Curvature, Quantum Theory, Relativistic Theory

Scientific paper

The Hamilton theorem that states that (under given conditions) a three-dimensional or four-dimensional Riemannian manifold can be smoothly deformed via a heat-type equation into a space of constant sectional curvature is discussed. Recently obtained compactness properties of the space of Riemannian structures are used to simplify the existing proof of the global nature of Hamilton's initial-value problem and to present it as a distinguished dynamical system on the space of Riemannian metrics. The connection between the renormalization group equation for nonlinear sigma models and the Hamilton initial-value problem is considered.

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