Multiplicative Differential Geometry

This book introduces multiplicative Frenet curves, investigates their local behaviors, defines multiplicative Bertrand curves, and introduces multiplicative rigid motions. It is suitable for graduate and undergraduate level courses in geometry and analysis, with examples and problems. It also explores multiplicative surfaces, differential forms, manifolds, and Einstein manifolds with applications in mathematical physics, classical geometry, economic theory, and time scale calculus.

Format: Hardback
Length: 360 pages
Publication date: 20 July 2022
Publisher: Taylor & Francis Ltd

This comprehensive book delves into the realm of multiplicative Frenet curves, providing a comprehensive introduction to this fascinating topic. It begins by defining multiplicative tangent, multiplicative normal, and multiplicative normal plane for a multiplicative Frenet curve, laying the foundation for further exploration. The author then delves into the local behaviors of a multiplicative parameterized curve around multiplicative biregular points, introducing concepts such as multiplicative Bertrand curves and investigating their properties. Additionally, a multiplicative rigid motion is introduced, offering a mathematical framework for studying the dynamics of multiplicative surfaces.

The book is designed to cater to a diverse audience, including instructors and graduate students, as well as specialists in geometry, mathematical physics, differential equations, engineering, and applied sciences. It serves as an excellent textbook for graduate and undergraduate-level courses in geometry and analysis, offering a wealth of examples and problems to reinforce the concepts presented.

The author begins by introducing the fundamental conceptions for multiplicative surfaces, including multiplicative first fundamental form, multiplicative rules for differentiations, and regularity conditions. An in-depth investigation of the main classes of multiplicative surfaces and second fundamental forms is conducted, shedding light on their properties and applications. Multiplicative differential forms, multiplicative manifolds, multiplicative Einstein manifolds, and their properties are explored, providing a deep understanding of this complex subject.

Furthermore, the book offers numerous unique applications in mathematical physics, classical geometry, economic theory, and theory of time scale calculus. The author demonstrates how multiplicative Frenet curves and their associated concepts can be applied to solve problems in these fields, offering valuable insights and solutions.

In conclusion, this book is a valuable resource for anyone interested in multiplicative surfaces and their applications. It provides a comprehensive and up-to-date introduction to the field, covering key concepts, theories, and applications. With its clear explanations, numerous examples, and problems, it is suitable for both students and professionals seeking to expand their knowledge in this area.

Weight: 664g
Dimension: 163 x 241 x 29 (mm)
ISBN-13: 9781032290607