This book introduces multiplicative Frenet curves. We define multiplicative tangent, multiplicative normal, and multiplicative normal plane for a multiplicative Frenet curve. We investigate the local behaviours of a multiplicative parameterized curve around multiplicative biregular points, define multiplicative Bertrand curves and investigate some of their properties. A multiplicative rigid motion is introduced.
The book is addressed to instructors and graduate students, and also specialists in geometry, mathematical physics, differential equations, engineering, and specialists in applied sciences. The book is suitable as a textbook for graduate and under-graduate level courses in geometry and analysis. Many examples and problems are included.
The author introduces the main conceptions for multiplicative surfaces: multiplicative first fundamental form, the main multiplicative rules for differentiations on multiplicative surfaces, and the main multiplicative regularity conditions for multiplicative surfaces. An investigation of the main classes of multiplicative surfaces and second fundamental forms for multiplicative surfaces is also employed. Multiplicative differential forms and their properties, multiplicative manifolds, multiplicative Einstein manifolds and their properties, are investigated as well.
Many unique applications in mathematical physics, classical geometry, economic theory, and theory of time scale calculus are offered.
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Postgraduate and Professional
Illustrationen
13 s/w Abbildungen, 13 s/w Zeichnungen
13 Line drawings, black and white; 13 Illustrations, black and white
Maße
Höhe: 240 mm
Breite: 161 mm
Dicke: 25 mm
Gewicht
ISBN-13
978-1-032-29060-7 (9781032290607)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Svetlin G. Georgiev is a mathematician who has worked in various areas of the study. He currently focuses on harmonic analysis, functional analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, integral equations, and dynamic calculus on time scales. He is also the author of Dynamic Geometry of Time Scales, CRC Press. He is a co-author of Conformable Dynamic Equations on Time Scales, with Douglas R. Anderson, and also: Multiple Fixed-Point Theorems and Applications in the Theory of ODEs, FDEs and PDE; Boundary Value Problems on Time Scales, Volume 1 and Volume II, all with Khalid Zennir and published by CRC Press.
1. Elements of the Multiplicative Euclidean Geometry
2. Multiplicative Curves in Rn
3. Multiplicative Plane Curves
4. General Theory of Multiplicative Surfaces
5. Multiplicative Fundamental Equations of a Multiplicative Surface
6. Special Classes of Multiplicative Surfaces
7. Multiplicative Differential Forms
8. The Multiplicative Nature Connection
9. Multiplicative Riemannian Manifolds
10. The Multiplicative Curvature Tensor
Appendix A. The Multiplicative Lipschitz Condition
Appendix B. The Multiplicative Implicit Function Theorem
