KeywordsRiemann Surface Tangent Plane Tangent Line Algebraic Curve Symmetric Pair
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- 1.J. V. Poncelet,Traité des propriétés projectives des figures, Mett-Paris 1822.Google Scholar
- 2.C. G. J. Jacobi,Über die Anwendung der elliptischen Transcendenten auf ein bekanntes Problem der Elementargeometrie, Gesammelte Werke, Vol.I (1881), pp. 278–293.Google Scholar
- 4.We shall allow the polygon to have self-intersections.Google Scholar
- 5.This may be verified analytically using the equations ofS andS' given below.Google Scholar
- 6.We note thatS ∩T p(S) is a plane conic containing a line, and hence must be two lines throughP as in Fig. 6. These lines are distinct since detQ#0.Google Scholar
- 7.SinceS∩(LΝL') contains and therefore is equal to the plane conicL+L', it follows thatLΝL' is the tangent plane toS atL∩L'. In particular,L 0, does not lie inLΝL' nor pass throughL∩L'.Google Scholar
- 8.We will comment on the construction in ℝ3 at the end of the paper.Google Scholar
- 9.The vertices are where three or more planes meet. In Fig. 8 these are the vertices of the shaded quadrilaterals.Google Scholar
- 10.This is the formulaK D=K M ⊗[D] D for the canonical line bundle of a smooth divisorD on a complex manifoldM.Google Scholar
- 11.That the intersection is transverse follows from the equations forS andS' given below.Google Scholar
- 12.In this connection M. Berger pointed out two papers by Cayley giving explicit conditions for Poncelet polygon to be closed. The references are Philosophical Magazine, vol. VI (1853), 99–102. and Philosophical Trans. Royal Soc. London, vol. CLI (1861), 225–239.Google Scholar
© Birkhäuser Verlag 1977