Revision #282 → #1540 · back to history
addedRiemann sphere (extended complex plane)0109d1d8451c
addedExtended complex numbersde65df92c17e
addedRiemann sphere as set of extended complex numbersea0b6b9dfe62
addedAddition on extended complex numbers6f78e0998a5d
addedMultiplication on extended complex numbers6acfe790b9d2
addedExtended complex numbers are not a field74f8d5a65aa6
addedDivision on extended complex numbers88672401b89c
addedRational functions extend continuously to the sphereb3a20a887cf2
addedRational functions are all holomorphic self-maps7aca13a319a3
addedExtending a specific rational function623f2a2c68b5
addedTransition map and Riemann sphere as complex manifold8ef1c1886455
addedRiemann surface746a120b52fb
addedSphere as one-point compactification of the planea6322af4a825
addedUniformization theoremdce5899a948d
addedUnique complex structure on the 2-sphere46d4533cafa4
addedComplex projective linef110787dd268
addedLines and conics biholomorphic to the projective line5a9fd6af416e
addedSphere via stereographic projectiondc939b704aec
addedUnit sphere diffeomorphic to Riemann sphere1391d61a8cd9
addedUnit circles and equator are identifiedc393229588b9
addedComplex structure determines metric up to conformal equivalence2854c700afbd
addedCorrespondence between complex structures and conformal classes59f1c4ac9151
addedExistence of complete constant-curvature metric17d0df06f27c
addedGauss–Bonnet forces positive curvature993c6db07532
addedRound metric on the Riemann sphere05264aa5ec54
addedAgreement with Fubini–Study metricb0af3e6cf670
addedUnique metric with 3-dimensional isometry group7758e309142c
addedAny metric conformally equivalent to round metric242d7cd823fd
addedAutomorphism of the Riemann sphereb260ff778342
addedAutomorphisms are exactly Möbius transformations35bf30ffae61
addedMöbius transformations as compositions6fc28bbf3567
addedGroup of Möbius transformations is PGLf75adc910c59
addedIsometries form a subgroup isomorphic to SO(3)ccb19e9cf643
addedMeromorphic function31633a948009
addedNo non-constant holomorphic maps on compact surfacesc5e41e406317