This book introduces plane curves on time scales. They are deducted the Frenet equations for plane and space curves. In the book is presented the basic theory of surfaces on time scales. They are defined tangent plane, \sigma_1 and \sigma_2 tangent planes, normal, \sigma_1 and \sigma_2 normals to a surface. They are introduced differentiable maps and differentials on surface.
This book provides the first and second fundamental forms of surfaces on time scales. They are introduced minimal surfaces and geodesics on time scales. In the book are studied the covaraint derivatives on time scales, pseudo-spherical surfaces and \sigma_1, \sigma_2 manifolds on time scales.
Table of Contents
1. Curves in Rn 2. General Theory of Surfaces 3. First Fundamental Forms 4. The Second Fundamental Forms 5. The Fundamental Equations of a Surface 6. Minimal Surfaces 7. The Delta Nature Connection A: Implicit Function Theorem References Index
Svetlin G. Georgiev (born 05 April 1974, Rouse, Bulgaria) is a mathematician who has worked in various areas of mathematics. He currently focuses on harmonic analysis, functional analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, integral equations, dynamic calculus on time scales. He is the author of several books for CRC Press, including Multiple Fixed-Point Theorems and Applications in the Theory of ODEs, FDEs and PDEs, Boundary Value Problems on Time Scales, Volume I and II, and co-author of Conformable Dynamic Equations on Time Scales.