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F

F F(F)

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A

F = dA

d A F

A = Adx

F = ,,

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F F = 0, (F)F = 0

K

K (A F)

K = 0, d K = 0;

F = s1s2 s2s1

s1 s2

F = ds1 ds2

A = s1ds2 + d

ds1 ds2

J =1

4dh d1 d2

h, 1, 2

dF = 0, d F = dh d1 d2

F = hd1 d2

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F = h (d1 d2)

dF = d (h (d1 d2)) = 0

R = (d1 d2)

R =1

2i

(1 + )2

R = 1

2i

1 + 2

dR = 0 d R = 0

R = d1 d2

R = du1 du2

= Sexp(i2) = Sexp(i2)

1 =1

1 + S2, 2 = , u1 =

1

1 + S2, u2 =

h = u1

F = u1R

F = u1 R = u1du1 du2 = d (u1)

2

2 du2

F

f = FJ = F

1

3! (J)

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f = (u1du1 du2)1

3!

1

4du1 d1 d2

f = u1u1u21

3!

1

4

du1 d1 d2 f = u1u1

1

3!

1

4u2u112

f =1

12u1u1FF

FF = 0

RR

= 0

J F = 0;

h = f(u1, u2)

JJ = 0

S3 S2

(r

, t) =

(Ax tz) + i(Ay + t(A 1))

(Az + tx) + i(A(A 1) ty)

(r, t) =(Ay + t(A 1)) + i(Az + tx)

(Ax tz) + i(A(A 1) ty)

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A =x2 + y2 + z2 t2 + 1

2

1 = 11 +

, 2 = 14i

ln(

)

u1 =1

1 + , u2 =

1

4iln(

)

2 u2

h = u1

F = R

1 +

(n)(r, t) =

(Ax tz) + i(Ay + t(A 1))

(Az + tx) + i(A(A 1) ty)

n

(n)(r, t) =

(Ay + t(A 1)) + i(Az + tx)

(Ax tz) + i(A(A 1) ty)

n

RR = R(R) = FF = F(F) = 0

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