Conformal geometry vs. projective geometry

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SUMMARY

Conformal geometry is a metric geometry, while projective geometry is not. The discussion highlights the relationship between these two geometries, specifically mentioning the stereographic projection as a connection to conformal geometry. Participants seek resources that clearly outline the relationships among various geometries, including affine, projective, Euclidean, hyperbolic, and conformal. Recommended readings include works by Schouten and Bill Burke, which provide in-depth explanations of these geometrical concepts.

PREREQUISITES
  • Understanding of metric geometry and its properties
  • Familiarity with projective geometry concepts
  • Knowledge of stereographic projection techniques
  • Basic comprehension of affine and hyperbolic geometries
NEXT STEPS
  • Research the properties of stereographic projection in conformal geometry
  • Study the relationships between affine, projective, and Euclidean geometries
  • Explore Schouten's works on Ricci calculus and its geometrical applications
  • Read Bill Burke's "Applied Differential Geometry" for practical insights
USEFUL FOR

Mathematicians, geometry enthusiasts, and students studying advanced geometry concepts will benefit from this discussion, particularly those interested in the relationships between different geometrical frameworks.

Lapidus
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How are those two geometries realeted?

Conformal geometry is a metric geometry. Projective geometry is not. But the stereographic projection is related to the conformal geometry.

Or does someone know a book/ notes where the individual geometries (affine, projective, euclidean, hyperbolic, conformal) are listed and the relationships among them is (neatly and well) explained?
 
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