Abstract
Let H denote the single sheeted hyperboloid with the unique (up to multiplicative constant) Lorentz metric, g, invariant under SL(2, ℝ), so g has constant non-zero curvature. We study the group Conf(H) of conformal diffeomorphisms of g, in particular the boundary behavior of the conformal factor fτ for τ ∈ Conf(H) and τ*g = fτg. We characterize those metrics in the conformal class of g which are of the form τ* g. This implies the determination of a solution of a certain hyperbolic partial differential equation by specifying boundary behavior at infinity.
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© 1988 Kluwer Academic Publishers
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Kostant, B., Sternberg, S. (1988). The Schwartzian Derivative and the Conformal Geometry of the Lorentz Hyperboloid. In: Cahen, M., Flato, M. (eds) Quantum Theories and Geometry. Mathematical Physics Studies, vol 10. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3055-1_7
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DOI: https://doi.org/10.1007/978-94-009-3055-1_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7874-0
Online ISBN: 978-94-009-3055-1
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