泊松流形、混合诱导丛和乘积G-空间上一些问题的讨论

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1、V

2、2℄℄;5℄FGtionsaregained.AtlastaboutsomepropertiesandequationsarediscussedonPoissonmanifold.Insection2,akindofnewinducedbundle–mixedinducedbundleisdefined,whichisdifferentfromthegivenbundleinbasemanifoldandfiberterm.Inaddition,thepropertiesoftheinduced

3、bundlearediscussed.Insection3,theproductG-spaceisdiscussedfromtheangleofproductmanifold.Keywords:Poissonmanifold;newoperatorζ;Poissonformalfield;mixedinducedbundle;productLiegroup;productGspaceIVTV

4、2℄℄;5℄FG"$=q7!y$4C~X?7(Hbx4C~H7(zbxqq9se

5、4Cqq%~X?TV℄Æq7!y
~uD&e-dwd(R;~!y86oq7!yA
q744.`1;ZB.Riemann

6、1854?V~B.7`

7、!yC~()9

8、xG℄jXRt=~4o2X'R~e-uR48VtXp9!y_a

9、$=e-℄
g8Vtl~4FdasManifoldq74F~
l<1$4C(#"'
VC

10、~>kq$}!Eo~q74~a6
*$rH.WeylRVj~ÆA℄G

11、~TheConceptsofRiemannSurfacesH.Whitney#"'~?ou!3~
nuq74uDe-9~G{

12、Ta
q74Ys?~4CF(~V=4C{9q74~t`Fso4C~(0
wq74~(Fw0
$D{o4C~WRPoisson!y$

13、#"'?oq74Y
%Sj~X-1CaPoisson!y$7

14、CTt~4Cg,6[!yCq

15、C
q7(9t?io-x4C(qC

16、(!~?'6#"'?o

17、x5?~%4XVtm#qVw:C9w~-Ca4CHsnso4q7hq7VTV

18、2℄℄;5℄FG/A.r4^/"tHA&}RPoisson!ysq7!yX-~Æ/

19、Poisson!yq
~ioAVaPoisson4
~ÆtueaHamilton`H)`~Hamilton`VtSse.~ioWeaHamilton`[*1)`ÆEu4Hamilton`Se.~4C

20、CG

21、Ca9V~4C12~ajVt3'8~eaHamilton`o[s3Poisson4
~;u4~eaHamilton`j
[rV~e-({V~sy/[eÆHamilton/V%74x~uwu~eaHamilton`

22、T~


23、/1950?W
m;ÆEhresmann#qugqSDX:q7Cees_Aug
~}ugq~V8rq7!ywqq;ZWS
XC~[q7!ywqq}SA&

24、S{ugue-~FVt#V~8rhDÆTUH$E4~-y
~XG(ue-$R;~e-8$#V~e-=4~j$X+~4C#X,x%ugYV4~8.1

25、&,#VjH3)~ugugq>

26、x%T~=8.$H.=(Whitney)E.6"(Stiefel)1935?fD~8nug~h
2Uo4>Xr$io
Vt8>X~"gkSstoiB~84M
~X"gπ:E−→M$X"e-

27、H!rMEA4−1

28、eR;j℄G$Xi

29、x∈M~"e-Ex=π(x)sVITV

30、2℄℄;5℄FGx~uy
$M~Yg[}
~Et~gXS)~g$gM×V,9V$X_~"e-(x,V),x∈M$x~u?~X$u
~8>X%SHX=_ami8nu~~=SH(~Yons>Xnug~4$,b*1sld~
}!0.3

31、xX3g=3

32、gugq
~ioy"B