Felix Klein and Sophus Lie on quartic surfaces in line geometry (Q6633327)

In this paper, the author explores the collaboration of the great German mathematician Felix Klein (1849--1925) and the Norwegian mathematician Sophus Lie (1842--1899) in general, and in particular on quartic surfaces in line geometry (for Klein's work on visualization of real algebraic curves and classification of cubic surfaces see [\textit{D. E. Rowe}, Arch. Hist. Exact Sci. 78, No. 4, 401--477 (2024; Zbl 07872241)]). The paper begins with the origins of line geometry in the work of Klein's mentor Plücker and discusses concepts like line coordinates and singularity surfaces. Klein's interactions with his teacher Clebsch and friend Noether in Göttingen preceded his first encounter with Lie in Berlin in the fall of 1869. The author gives a detailed account of the joint work of Klein and Lie, first in Berlin and then followed by their sojourn in Paris in 1870.\N\NFor historians this is an important paper since the collaboration of the two mathematicians is presented from the aspect of line geometry and not as usual from group theory.\N\NOther topics discussed are Fresnel's surface and Kummer surfaces, higher metric geometry, Lie's work on line and sphere complexes and Weiler's classification of quadratic complexes.