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1


1

1.

O S1

E=A r/r3dS1, dS2,Od,dS1,dS2

S0OS1


1

S0=S1=A

A=q/4(q),

(q) S 0=q / 4.


1

E=A r/r3O

S0POPS0ppS1;OPS0pS1

S1=,Fy=S1A.

O S1


2 mobius

2.Mobius

d=nS

Mobius


Mobius s 1 y as 1

MobiusS1y =AS1.

O S1


3 klein

3. Klein


1

  • LL

  • O


L m m dx m dx m m m m 0 4 a o

LMMdxMdxM"

MM`M"04A(O)


1


P a b c

PABC


4 3 5

435


1

L

M1qM2q

M2=4A+M1

P1=0;P2=4A;

1=P1-M1= -M1;

2=P2-M2=4A-4A+M1)=-M1=1

qM


Klein

Klein


A 1 2 3

A

=|1|-|2|+|3|.

4.(Mobius)


Cdef cdhg 3 3 2 2 2

cdefcdhg

|3|=|3|+||;|2|=|2|-||;

=+2||.


Y 1 2 3 y 1 2 3 y

y=|1|+|2|+|3|,

y'=|1|+(|2|-||)

+(|3|+||)=y


1


1

OS0S1=4 y=4AOS0S0=0 y=0

y

.


1

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