Sophus Lie and Felix Klein: The Erlangen Program and Its Impact in Mathematics and Physics
Editors
Lizhen Ji
University of Michigan, Ann Arbor, USAAthanase Papadopoulos
Université de Strasbourg, France
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p. v PrefaceLizhen JiAthanase Papadopoulos
pp. vii–viii Contentspp. xi–xviii IntroductionLizhen JiAthanase Papadopoulos
pp. 1–26 Sophus Lie, a giant in mathematicsLizhen Ji
pp. 27–58 Felix Klein: his life and mathematicsLizhen Ji
pp. 59–75 Klein and the Erlangen ProgrammeJeremy J. Gray
pp. 77–90 Klein’s “Erlanger Programm”: do traces of it exist in physical theories?Hubert Goenner
pp. 91–136 On Klein’s "So-called Non-Euclidean geometry"Norbert A’CampoAthanase Papadopoulos
pp. 137–190 What are symmetries of PDEs and what are PDEs themselves?Alexandre Vinogradov
pp. 191–216 Transformation groups in non-Riemannian geometryCharles Frances
pp. 217–235 Transitional geometryNorbert A’CampoAthanase Papadopoulos
pp. 237–245 On the projective geometry of constant curvature spacesAthanase PapadopoulosSumio Yamada
pp. 247–281 The Erlangen program and discrete differential geometryYuri B. Suris
pp. 283–306 Three-dimensional gravity – an application of Felix Klein’s ideas in physicsCatherine Meusburger
pp. 307–324 Invariances in physics and group theoryJean-Bernard Zuber