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Geometrical Structures and the Grinding Process for Three Plates

  • D. P. L. Castrigiano

Abstract

The Grinding Process of Three Plates (GTP), which is discussed in the philosophy of science chiefly by Dingier, Lorenzen and the protophysicists, is defined mathematically within the frame of Riemannian geometry. For this the notions of geodesic rigidity at a point which generalizes that of isometric rigidity, and of a dingler surface which describes the surfaces generated by GTP, are introduced. It is proved that GTP can be carried out if and only if the space has constant curvature. Furthermore, in this case the generated surfaces are just the totally geodesic hypersurfaces.

Keywords

Symmetric Space Sectional Curvature Constant Curvature Parallel Transport Riemannian Space 
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Copyright information

© Plenum Press, New York 1981

Authors and Affiliations

  • D. P. L. Castrigiano
    • 1
  1. 1.Institut für MathematikTechnischen Universität MünchenMünchen 2Federal Republic of Germany

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