by Krishan L Duggal (University of Windsor, Canada) & Dae Ho Jin (Dongguk University, Korea)

Table of Contents (74k)
Preface (62k)
Chapter 1: The concept of null curves (179k)

This is a first textbook that is entirely focused on the up-to-date developments of null curves with their applications to science and engineering. It fills an important gap in a second-level course in differential geometry, as well as being essential for a core undergraduate course on Riemannian curves and surfaces. The sequence of chapters is arranged to provide in-depth understanding of a chapter and stimulate further interest in the next. The book comprises a large variety of solved examples and rigorous exercises that range from elementary to higher levels. This unique volume is self-contained and unified in presenting:

• A systematic account of all possible null curves, their Frenet equations, unique null Cartan curves in Lorentzian manifolds and their practical problems in science and engineering.

• The geometric and physical significance of null geodesics, mechanical systems involving curvature of null curves, simple variation problems and the interrelation of null curves with hypersurfaces.

• The Concept of Null Curves
• Null Curves in Lorentzian Manifolds
• Null Curves in Semi-Riemannian Manifolds
• Geometry of Null Cartan Curves (Unique Existence Theorems)
• Applications: Null Soliton Solutions in 3D and 4D
• Mechanical Systems and 3D Null Curves
• Lightlike Hypersurfaces
• Geometry and Physics of Null Geodesics