9339

8621

كارشناسي ارشد

علوم رياضي- رياضي محض

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1393

هفت،81ص.مصور

ص.ع.به فارسي و انگليسي

قهرمان طاهريان

اعظم اعتماد دهكردي

17/9/93

مجتبي آقايي فروشاني، محمدرضا كوشش

رياضي

ID8621

Flat Laguerre planes of Kleinewillingh fer type III B samira bozorgpoor s bozorgpour@math iut ac ir 2014 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Sayed Ghahreman Taherian taherian@cc iut ac ir Advisor Dr Azam Etemad Dehkordy ae110mat@ cc iut ac ir 2010 MSC 51H15 51B15 Keywords Laguerre planes Kleinewillingh fer type Automorphism Abstract Originally the classical Laguerre plane was de ned as the geometry of the oriented lines and circlesin the real euclidean plane Like a projective plane a Laguerre plane is a type of incidence structure de ned in terms of sets of elements and an incidence relationship between them The most importantobjects of a Laguerre plane are generally called points generators and circles with the circles andgenerators being sets of points Perhaps the most straightforward model of a Laguerre plane uses theunit cylinder S 1 R in R3 The set of points P consists of the points on this cylinder the set ofcircles C consists of the circles and ovals formed by intersections of the cylinder with any non verticalplanes and the set of generators G consists of the generators of the cylinder Points are incident withcircles and generators in the standard way The rst model of Laguerre plane was given by Benz and M urer In the Euclidean plane we de ne aspear as an oriented line so that each Euclidean line underlies two spears pointing in opposite direc tions A cycle is either a single point a point cycle or an oriented circle a proper cycle that workslike the oriented line with each Euclidean circle underlying clockwise and counter clockwise cycles Just like Lenz Barlotti classes re ect transitivity properties of certain groups of central collineationsin projective planes Kleinewillingh fer types re ect transitivity properties of certain groups of centralautomorphisms in Laguerre planes An important class of Laguerre planes are at planes A at or2 dimensional Laguerre plane L Z C is an incidence structure of points and circles whose pointset is the cylinder Z S1 R where S1 usually is represented as R whose circles C C are

قهرمان طاهريان

اعظم اعتماد دهكردي

مجتبي آقايي فروشاني، محمدرضا كوشش