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