The General Projective Theory of Curves

The present memoir is mainly a collection of the author's works in a period of four years since 1937. It consists of six chapter. Chapter 1 is concerned with the theory of plane curves, containing the constructions of projective normal worked out by T.C. Fon and S.C. Chang as well as C.C. Hsiung's research on the contact invariants of two plane curves.

Chapter 2 is devoted to the researches on certain singularities of a plane curve with applications; it constitutes the most important part of the present memoir. The establishment of the projective theory of representable singularities is, on the one hand, fundamental for the development of the whole schedule of the memoir, while the theory of singularities and, especially, non-representable singularities worked out by S.C. Chang is, on the other hand, of great importance for further development.

First of all, the theory of representable singularities is utilized in treating the projective differential geometry of curves in ordinary space (Chapter 3), showing that the whole theory can be established by means of a purely geometrical method. Chapter 4, the same method is applied to the theory of intersection-variants of two space curves. In Chapter 5, established the projective differential geometry of curves in space of four dimensions. Finally, chapter 6 is shown the existence of a sequence of normal curves, which play an important role in the general projective theory of curves in space of higher dimensions.

Book: The General Projective Theory of Curves - Su Bu-chin - the Science Press

Admin 08 April 2016 Book