عنوان :
توپولوژي رويه ها با سايه هاي همبند
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي محض﴿هندسه﴾
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان،دانشكده علوم رياضي
يادداشت :
ص.ع.به فارسي و انگليسي
استاد راهنما :
اعظم اعتماد
استاد مشاور :
محمدرضا كوشش
توصيفگر ها :
عدد مرئي , طوقه هاي اريب , شاخص مماسي , نگاشت گاوسي , خاصيت دوتكه اي
تاريخ نمايه سازي :
21/2/89
استاد داور :
عاطفه قرباني،امير هاشمي
چكيده فارسي :
به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي
چكيده انگليسي :
Topology of Surfaces with Connected Shades Hajar Haem Haem40@gmail com March 17 2010 Master of Science Thesis in Farsi Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisor Dr Azam Etemad ae110mat@cc iut ac ir2010 MSC 14J80 Key words Shade Vision Number Skew Loop Tantrix Gauss Map Two Piece Property AbstractIn this thesis we present an construction to all orientable closed surfaces and prove that anyclosed orientable surface may be smoothly embedded in Euclidean 3 space so that when itis illuminated by parallel rays from any direction the shade cast on the surface is connected In particular this problem gives counterexample of every genus to a conjecture of J Choe 5 states that any immersion of a surface of topological genus g should have at least oneshade with g 1 components Note that M has connected shades if and only if the guass map of M satis es a two piece property a set A in E n is said to have the two piece property if and only if every hyperplanein E n cuts A into at most to pieces The study of shades is also of substantial interest in computer vision where shape fromshading problems are studied extensively One of basic questions that considered by H Wente in 1978 is Does connectedness of eachof the shades Su of a closed orientable surface M imply that M is convex M Ghomi showedthat the answer is yes provided that either M is imply connected otherwise it was provedthat the answer is no by constructing smooth embedded tori with connected shades Also the rst proposition in main chapter of this thesis is concerned with the existence ofclosed curves without any pairs of parallel tangent lines i e skew loops and is an extensionof a construction rst discovered by B Segre It was shown that a tubular surface abouta skew loop has connected shades Here we show that one may construct a skew loop sothat the corresponding tubular surface has any desired number of pairs of points which awayfrom each other we will then prove our second proposition which states that if a surfacewith connected shades has a pair of points p q which face away from each other then onemay add a handle to that surface and thus increase its topological genus while preserving theconnectedness of each of its shades More precisely we will delete small neighborhoods of p and q which are homeomorphic todisks and glue in their place a topological annulus To this end we rst deform neighborhoods of p and q until they coincide with pieces of spheresof the same radius and then cut small disks from these spherical pieces It will be shownthat the resulting surface still has connected shades We join the two boundary components of this surface with a surface of revolution which wecall an hour glass The hour glass has the crucial property that each component of each ofits shades intersects its boundary This implies that our nal surface will have connected shades 1
استاد راهنما :
اعظم اعتماد
استاد مشاور :
محمدرضا كوشش
استاد داور :
عاطفه قرباني،امير هاشمي
