de Sitter空间中一类类空子流形的刚性及Schrodinger算子的第一特征值.pdf

《de Sitter空间中一类类空子流形的刚性及Schrodinger算子的第一特征值.pdf》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、a¬ÆØ©M.D.ThesisdeSitter˜m¥˜aa˜f6/f59Schr•odingerŽf1˜AŠRigidityandthersteigenvalueofSchr•odingeroperatorsforaclassofspacelikesubmanifoldsindeSitterspacesܬ¬ZhangJingjing8¹ÕM5(²...........................................................iÁ‡..........................................................

2、........iiAbstract..............................................................iiicó.................................................................1x1ý•£.........................................................4x2deSitter˜m¥÷vR=aH+ba˜f6/..............82.1Úó9̇(J..............................

3、...........................82.2̇Úny².........................................................102.3̇½ny².........................................................14x3;—a˜f6/¥Schr•odingerŽf1˜AŠ.................173.1Úó9̇(J.........................................................173.2̇Úny².....

4、....................................................183.3̇½ny².........................................................21ë•©z.............................................................25—..................................................................291ÕM5(²<(²¤¥Ø©´·‡<3“•e?1ïÄóŠ9ïÄ

5、¤J"¦·¤•§Ø©¥AO±I5Ú—/•§Ø©¥Ø•)Ù¦<®²uL½>LïĤJ§•Ø•¹•¼Ü“‰ŒÆ½Ù¦˜ÅƽyÖ¦^Lá"†·˜ÓóŠÓ“éïĤ‰?Ûzþ®3Ø©¥Š²(`²¿L«¿"¶µFϵ'uØ©¦^Ç`²<)Ü“‰ŒÆk'3!¦^ÆØ©5½§=µÆk3xØ©E<‡§#NØ©Ú/¶ÆŒ±úÙØ©ܽܩSN§Œ±æ^K

6、ÏLéa˜f6/²þ•ÇÚIOêþ•Ç?1·•›,Ta˜f6/´ß½öåu˜‡V•Î¡H1(sinhr)Sn1(coshr)¿©^‡.Ø©
©•n!:1˜!´ý•£,0deSitter˜m¥a˜f6/ÄVgÚÄúª.n+p1!ïÄdeSitter˜mSp(c)¥IOêþ•ÇRÚ²þ•ÇH÷v‚5'XR=aH+ba˜f6/Mn,‰ÑMn´ß½öåu˜‡V•Î¡¿©^‡.äN„½n2.1,½n2.2.1n!ïĽÂ3deSitter˜mSn+pnþSchr-p(c)¥;—a˜f6/M•odingerŽfLH;LRAŠO,Š•A^‰ÑTa˜f6/´

7、ß¿©^‡.äN„½n3.1,½n3.2.'''………ccc:deSitter˜m;a˜f6/;ß;V•Î¡;Schr•odingerŽf;AŠ;IOêþ•Ç;²1²þ•Ç•þ;²1ü²þ•Ç•þ.iiAbstractInthisarticle,wemainlystudythespacelikesubmanifolds(compactorcomplete)inn+pthedeSitterspaceSp(