Abstract
Preface
Preliminaries
order and type of submanifolds
Submanifolds of nite type [31]
Surfaces with nite type Gauss map
Minimal polynomial criterion
Deformation minimal principle
Frenet Surfaces with Pointwise 1??Type Gauss Map
Geometric concepts
Special ruled surfaces of nite type
Darboux developable ruled surface M7 with pointwise 1??type Gauss map of rst kind
The Finiteness property of tangential Dar- boux developable ruled surface M8 with 1??type Gauss map
The Finiteness property of rectifying Dar- boux developable ruled surface M9
Finite Type of the Pedal of Revolution Surfaces in E3
Basic concepts
Pedal of the revolution surfaces of polyno- mial kind
Pedal of the revolution surfaces of rational kind
Special revolution surfaces
Finiteness Property of Deformed Revolution Surfaces in E3
Deformation for revolution surfaces in E3
Finiteness property of the mean curvature ow
Finiteness property of isothermal revolu- tion surfaces
General examples
Garay’s Condition of Deformed Cylindrical and Translation Surfaces in E3
Cylindrical surfaces in E3
Translation surfaces in E3
Conclusion
Future Work
Bibliography
Appendix
Arabic Summary
الفهرس 
