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Projective Compactification of \(\mathbb {R}^{1,1}\) and Its Möbius Geometry

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Abstract

We examine the semi-Riemannian manifold \(\mathbb {R}^{1,1}\), which is realized as the split complex plane, and its conformal compactification as an analogue of the complex plane and the Riemann sphere. We also consider conformal maps on the compactification and study some of their basic properties.

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Authors and Affiliations

  1. Department of Mathematics, The Florida State University, 208 Love Building, 1017 Academic Way, Tallahassee, FL, 32306-4510, USA

    John A. Emanuello & Craig A. Nolder

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  1. John A. Emanuello
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  2. Craig A. Nolder
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Correspondence to John A. Emanuello.

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Communicated by Michael Shapiro.

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Emanuello, J.A., Nolder, C.A. Projective Compactification of \(\mathbb {R}^{1,1}\) and Its Möbius Geometry. Complex Anal. Oper. Theory 9, 329–354 (2015). https://doi.org/10.1007/s11785-014-0363-5

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  • DOI: https://doi.org/10.1007/s11785-014-0363-5

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