پديد آورنده :
الماسي، ايوب
عنوان :
رويه هاي خط كشي شده در E4
مقطع تحصيلي :
كارشناسي ارشد
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
نه،85ص.: نمودار
يادداشت :
ص.ع.به فارسي و انگليسي
استاد راهنما :
اعظم اعتماد
توصيفگر ها :
رويه هاي خط كشي شده در فضاي چهاربعدي اقليدسي , انحناي گاوسي و متوسط , رويه ي مينيمال , بيضي انحنا , ابرهمديس , رويه چن
تاريخ نمايه سازي :
10/4/93
استاد داور :
امير هاشمي، قهرمان طاهريان
چكيده انگليسي :
Ruled surfaces in E4 Ayob Almasi a almasi@math iut ac ir 8 January 2014 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Azam Etemad Dehkordy ae110mat@cc iut ac ir Advisor Dr Mansour Aghasi m aghasi@cc iut ac ir 2010 MSC 62Kxx 62K05 62K10 Keywords Ruled surfaces in four dimensional Euclidean Gaussian and mean curvature Minimalsurface curvature ellipse Superconformal Chen surfaces AbstractDi erantial geometry of ruled surfaces has been studied in classical geometry using various approaches In 1936 Plass studied ruled surface in E 4 In the present study we consider ruled surfacs imbeddedin the Euclidean space of four dimension For this purpose we calculate the Gaussion and meancurvature of ruled surfacs in the Euclidean space of four dimension and give some special example ofruled surface in E 4 We explain some geometric properties of this surfaces in E 4 For this purpose weintroduce the coe cients of the rst and second fundamental form We also introduce the Chrito elsymbles of ruled surface in the E 4 A ruled surface M in the Euclidean space of four dimension E 4maybe considered as a surface that generated by a vector moving along a curve We say that a surfacein E n is minimal if its mean curvature vanishes identically so we show that the only minimal ruledsurfaces in E 4 are those of E 3 namely the right helicoid We derive the Ferent fram in E 4 and calculatethe Gaussion curvature for ruled surfaces With an arthonormal basis of the tangent spase Tp M atpoint in p M we de ne the unit vector of the normal section We also de ne the ellipse of curvature Functions associated to the coe cients of the second fundamental form expresse the point p of ruledsurface in E 4 inside outside or is on ellipse of curvature We also show that the origin p of Np Mis non degenerate and lies on the ellipse of curvature The characterization of point in the surface aselliptic parabplic hyperbolic point and the in ection point are also discussed We show that ellipseof curvature can be degenerate into a line segment or a point Using of the di nition of the ellipse ofcurvature we de ne superconformal surface as the surface for which ellipse of curvature is a circle
استاد راهنما :
اعظم اعتماد
استاد داور :
امير هاشمي، قهرمان طاهريان
