Surfaces in Classical Geometries

Gary R. Jensen is currently professor of mathematics at Washington University in St. Louis, Missouri. Emilio Musso is professor of mathematics at the Politecnico di Torino, Torino, Italy and Lorenzo Nicolodi is professor of mathematics at the Univerita di Parma, Parma, Italy.

• 1. Introduction.- 2. Lie Groups.- 3. Theory of Moving Frames.- 4. Euclidean Geometry.- 5. Spherical Geometry.- 6. Hyperbolic Geometry.- 7. Complex Structure.- 8. Minimal Immersions in Euclidean Space.- 9. Isothermic Immersions.- 10. The Bonnet Problem.- 11. CMC 1 Surfaces in H3.- 12. Möbius Geometry.- 13. Complex Structure and Möbius Geometry.- 14. Isothermic Immersions in Möbius Space.- 15. Lie Sphere Geometry.- Solutions to Select Problems.- References.- Index.

"300 problems and exercices, from simple until open problems, are contained in this book and they are the essential part of it. In conclusion, it is an interesting book written carefully and with originality. Undoubtedly its reading will be very helpful to any geometer." (Charalampos Charitos, zbMATH 1347.53001, 2016)