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.
