Аналитическая геометрия. Часть III. Многомерные пространства. Гиперповерхности второго порядка. Шурыгин В.В. - 59 стр.

UptoLike

Составители: 

Φ Ψ
Φ = Ψ
Φ = Ψ ` Φ` = Ψ`
` x
1
= t x
i
= 0 i = 2, . . . , n
a
11
(x
1
)
2
+ 2a
1 n+1
x
1
+ a
n+1 n+1
= 0 b
11
(x
1
)
2
+ 2b
1 n+1
x
1
+ b
n+1 n+1
= 0
a
11
b
11
=
a
1 n+1
b
1 n+1
=
a
n+1 n+1
b
n+1 n+1
.
x
1
= t x
2
= t x
i
= 0 i = 3, . . . , n
Φ Ψ A
n
α GA(A
n
) α(Φ) = Ψ A
C
n
1) Φ A
2
1
9
2) A
2
1
9
Φ {O; e
i
}
Ψ {O
0
; e
0
i
} α : A
2
A
2
α(O) = O
0
bα(e
i
) = e
0
i
Φ Ψ
Φ {O; e
i
}
F (x
1
, x
2
) = 0 1
9
α(Φ) = Ψ
α : A
2
A
2
Ψ {α(O); bα(e
i
)}
F (x
1
, x
2
) = 0
A
3
1) Φ A
3
90.*3.-B*3C,-/7> Φ  5 B7-3-* F 90.*3.-B*3C,-/7> Ψ <
   /60 235B,*,08 .3-.-3½0-,56>,A  7-  -)*B0D,-  Φ = Ψ <
   /60 Φ = Ψ  7- D68 6‡+-” .38:-” ` 0:**7 :*/7- 35B*,/7B- Φ∩` = Ψ∩` <
 A+0358 .38:2‡ ` / 235B,*,08:0 x1 = t  xi = 0 .30 i = 2, . . . , n  .-62
)0: /-B.5D5‡ˆ0* :,-“*/7B5 7-)*1  E5D5B5*:A* 1B5D357,A:0 235B,*,08
:0 a11(x1)2 + 2a1 n+1x1 + an+1 n+1 = 0 0 b11(x1)2 + 2b1 n+1x1 + bn+1 n+1 = 0 <
7/‡D5 /6*D2*7 )7-
                          a11   a1 n+1   an+1 n+1
                              =        =          .
                          b11   b1 n+1   bn+1 n+1
  53>0328 235B,*,08 .38:-” •BA+0358  ,5.30:*3  ,5 /6*D2‡ˆ*: ‰59* .38
:2‡ / 235B,*,08:0 x1 = t  x2 = t  xi = 0 .30 i = 3, . . . , n‹ .-62)0: .3-
.-3½0-,56>,-/7> B/*C 1-¨„„0½0*,7-B < ’-6,-* D-15E57*6>/7B- ¨7-9- 27B*3
“D*,08 :-“,- ,5”70 B Šà •/:< 7*-3*:2 ,5 / < ²IH‹< 
   VWXYZY[Y\]Y^  km xaemfegkmfrbghia kigfgxg egftnvj Φ a Ψ k A bjlcp
kj{iht j``abbg zvkakjombibcdaw mhoa h}qmhik}mi j``abbgm nkaymbam
                                                                       n


                   v
α ∈ GA(An ) w efa gigfgd α(Φ) = Ψ k AC     n €
    Y—XYœ^ 1) ¹htvjt vfakjt kigfgxg egftnvj Φ k A2 dgymi |ci‚ ljp
njbj gnbad a igo‚vg gnbad }fjkbmbamd al heahvj 1◦ 9◦ €
            v                      nv                   v
   2)  km fakcm kigfgxg egft j k A2 j``abbg z kakjombibc igx j a
                                                                          n
igo‚vg igxnjw vgxnj k bmvgigfcr j``abbcr hahimdjr vggf nabji gba ljp
nj{iht gnbad a imd ym }fjkbmbamd al heahvj 1◦ 9◦ €
   £—™œ¤œšY[¥˜š›—^ ’*3B-* 27B*3“D*,0* /6*D2*7 0E D-15E5,,-9- BA‰* .3*D
6-“*,08 < -15“*: B7-3-* <
   /60 235B,*,0* 130B-” Φ B 3*.*3* {O; e } /-B.5D5*7 / 235B,*,0*: 130
B-” Ψ B 3*.*3* {O0; e0i}  7- 5„„0,,-* .3*-+35E-B5,0* α : A2 → A2  -.3*
                                             i


D*68*:-* 2/6-B08:0~ α(O) = O0  αb(ei) = e0i  .*3*B-D07 Φ B Ψ <
   +357,-  .2/7> 130B58 Φ 0:**7 B 3*.*3* {O; e } ,*1-7-3-* 235B,*,0*
               0E /.0/15    ◦ ◦ 0           .30  ,*1-7-3-:    5„„0,,-: .3*
                                                      i
    1 2
F (x , x ) = 0            1 9       α(Φ) = Ψ
-+35E-B5,00 α : A2 → A2 < -9D5 130B58 Ψ B 3*.*3* {α(O); αb(ei)} 0:**7 7-
“* /5:-* 235B,*,0* F (x1, x2) = 0 < 
   ,56-90),58 7*-3*:5 0:**7 :*/7- D68 .-B*3C,-/7*” G 9- .-38D15 B A <
                ¹                                   n
    Y—XYœ^ 1) htvjt egkmfrbghi‚ kigfgxg egft vj Φ k A3 dgymi |ci‚
                                                                            3


ljnjbj gnbad a igo‚vg gnbad }fjkbmbamd al homn}{qmxg baym heahvj al
                                       ÀÏ