Corpus ID: 14138711

Pseudospheres in geometry and physics: from Beltrami to De Sitter and beyond ∗

  title={Pseudospheres in geometry and physics: from Beltrami to De Sitter and beyond ∗},
  author={B. Bertotti and R. Catenacci and C. Dappiaggi},
  journal={arXiv: History and Overview},
  • B. Bertotti, R. Catenacci, C. Dappiaggi
  • Published 2005
  • Mathematics, Physics
  • arXiv: History and Overview
  • We review the extraordinary fertility and proliferation in mathematics and physics of the concept of a surface with constant and negative Gaussian curvature. In his outstanding 1868 paper Beltrami discussed how non-Euclidean geometry is actually realized and displayed in a disk on the plane. This metric is intrinsically defined and definite; but only if indefinite metrics are introduced it is possible to fully understand the structure of pseudospheres. In a threedimensional flat space R 3 the… CONTINUE READING
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