8473

7854

كارشناسي ارشد

رياضي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1392

هشت،86ص.

ص.ع.به فارسي و انگليسي

اعظم اعتماد

منصور آقاسي

8/11/92

قهرمان طاهريان، فريد بهرامي

رياضي

ID7854

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

Generalized Rotation Surfaces in E4 Samira Khani s khani@math iut ac ir 06 08 2013 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Azam Etemad ae110mat@ cc iut ac ir Advisor Dr Mansour Aghasi m aghasi at cc iut ac ir 2010 MSC 53C40 53C42 Keywords Ruled surface Rotation surface Tensor product surface Chen surface AbstractIn the present study we consider generalized rotation surfaces imbedded in an Euclidean space offour dimension So we give some basic concepts of the surfaces in E4 such as the coe cients of the rst fundamental form and some special examples of these surfaces in E4 Further the curvatureproperties of these surfaces are investigated We consider Frenet curve with constant curvature Sincethese curves are trajectories of the 1 parameter group of the Euclidean transformations so Kleinand lie called them W curves We explain some geometric properties of W curves In 2008 Ganchevand Milousheva considered the surface M generated by a W curve in a Euclidean 4 space Thiscurve is a generalization of the circular helix in an Euclidean space of three dimensions They haveshown that these generated surfaces are a special type of rotation surfaces which are introduced rstby C Moore in 1919 We give a necessary and su cient condition for a W curve on a trous to betwisted We consider ruled surfaces imbedded in a Euclidean space of four dimensions In 1936 Plassstudied ruled surfaces imbedded in E4 In 1980 Rouxel considered ruled Chen surfaces in E4 Wealso calculate the Gaussian and mean curvature vector of generalized rotation surfaces and give anecessary and su cient condition for vanishing Gaussian and mean curvature We de ne Vranceanurotation surface and Cli ord torus and tensor product surface of two Euclidean planer curves in aEuclidean 4 space We show that tensor product surface of two Euclidean planar curves is a minimalsurface in E4 if and only if one of curves is a straight line through 0 In 1973 Chen de ned the alliedvector eld a v of a normal vector eld v In particular the allied mean curvature vector eld isorthogonal to H Further B Y Chen de ned the A surface to be the surface for which a H vanishesidentically Such surfaces are also called Chen surfaces The class of Chen surfaces contain all minimal

اعظم اعتماد

منصور آقاسي

قهرمان طاهريان، فريد بهرامي