Minkowski空間及其二次曲面上的完全Poncelet定理.pdf

1、西北大學(xué)碩士學(xué)位論文Minkowski空間及其二次曲面上的完全Poncelet定理姓名：王耀雄申請(qǐng)學(xué)位級(jí)別：碩士專(zhuān)業(yè)：理論物理指導(dǎo)教師：石康杰20090401AbstractPoncelet’StheoremisafamoustheoremingeometrywhichreferstoastraightlinereflectselasticallyonanellipseandthepropertiesitpossessesEspecia

2、llyifthetrajectoryofthelineformsaclosedpolygonafterPbouncesontheboundarythenwecanobtainPonceletstheoremintwo—dimensionalspace，andthepolygoniscalledPoncelet’SpolygonWecanrelatethistheoremtosomepracticalphysicalproblems：on

3、eparticlemovesfreelyinsomespaceandbounceselasticallyonaquadricboundaryinthisspace，thenwecantreatthefreeparticleasthestraightlineandthereflectionasthebounceonboundaryThesesystemsarebilliardsystemsThesimilaritybetweenPonce

4、let’StheoremandquadricbilliardsystemfacilitateUSusingtheseresultstodescribethepropertiesoftheparticleWeCanalsoextendPoncelet’Stheoremtohigh—dimensionalspacesandderivecorrespondingresultsonrestrictedquadricsurfacesBythede

5、velopmentofsuperstringtheoryandcosmologydynamicalpropertiesofAdSspacesanddSspacesattractmoreandmoreinterestBecauseofAdSspacesanddSspacescanbetreatasquadricsurfacesinhigh—dimensionalMinkowskispaces，weCananalysethemotionof

6、afreeparticleinthesespacesbyPoncelet’StheoremThemainresultsofthisthesisareasfollows：Fromdifferentperspectives，wediscussthereflectionofafreeparticleonahyperplaneinaMinkowskispace，andderivethecorrespondingreflectionlawwhic

7、hisconsistentwithitsdefinitioninprojectivegeometryThenwegeneralisePoncelet’StheoremandfullPoncelet’Stheoremtohigh—dimensionalMinkowskispacesandtheirquadricsurfacesincludingAdSspacesanddSspacesInaddition，Ialsointroducesom