Multiplicative Differential Geometry - Hardcover

Georgiev, Svetlin G.

Hardcover

ISBN 10: 1032290609 ISBN 13: 9781032290607

Publisher: Chapman and Hall/CRC, 2022

Synopsis

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.

About this title

About the Author

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.

Edition details

• Publisher: Chapman and Hall/CRC
• Publication date: 2022
• Language: English
• ISBN 10: 1032290609
• ISBN 13: 9781032290607
• Binding: Hardcover
• Edition number: 1
• Number of pages: 360