الفهرس يوجد فقط 14 صفحة متاحة للعرض العام
 |  | from | 127 |  |  |
| | | from | 127 | | |
المستخلص
The aim of this thesis is to relate the study of evolutions of curves and surfaces and integrability of evolutionary partial differential equations
The thesis is divided into five chapters:
The first chapter considered as an introductory one, where the differential geometry of curves in , ,and characteristic prosperities of soliton equations are introduced .Also some examples of solitons as models for integrable systems are presented. Differentiable manifolds, Finally differential forms and their operations Jet bundles and exterior calculus and differentiable
manifold are defined.
Chapter two is devoted to the relationship between space- like curve with space – like principal normal and soliton equations in Minkowski 3- space
Chapter three contains the a relationship between curve evolution and soliton equations in Euclidean 4- space.
In chapter four we introduce a relationship between curve evolution and suggested integrable equations in Minkowski 4- space.
Finally, In chapter five we discuss the relation between surfaces and soliton equations in as well as in and higher dimension solitons.
Some new results that appeared in chapter two, three and four are formulated in research papers submitted for publication.