Аналитическая геометрия. Часть III. Многомерные пространства. Гиперповерхности второго порядка. Шурыгин В.В. - 93 стр.

UptoLike

Составители: 

1
. (x
1
)
2
+ (x
2
)
2
+ (x
3
)
2
+ (x
4
)
2
= 0 ( )
2
. (x
1
)
2
+ (x
2
)
2
+ (x
3
)
2
(x
4
)
2
= 0 (
)
3
. (x
1
)
2
+ (x
2
)
2
(x
3
)
2
(x
4
)
2
= 0 (
)
4
. (x
1
)
2
+ (x
2
)
2
+ (x
3
)
2
( )
5
. (x
1
)
2
+ (x
2
)
2
(x
3
)
2
( )
6
. (x
1
)
2
+ (x
2
)
2
= 0 (
x
1
= x
2
= 0)
7
. (x
1
)
2
(x
2
)
2
= 0 (
)
8
. (x
1
)
2
= 0 ( )
P
2
P
3
2
A
3
=
P
3
\ P
2
3
5
2
3
5
2
3
5
P
n
P
n
P
n
π P
n
p(V
n
(π)) V
n
(π) V
n+1
   1◦ . (x1 )2 + (x2 )2 + (x3 )2 + (x4 )2 = 0 ( dbadjt gkjo‚bjt egkmfrbghi‚) 
   2◦ . (x1 )2 + (x2 )2 + (x3 )2 − (x4 )2 = 0 ( kmqmhikmbbjt gkjo‚bjt egkmfrp
bghi‚) 
                                                      u       v      n
   3◦ . (x1 )2 + (x2 )2 − (x3 )2 − (x4 )2 = 0 ( oabm sjijt go‚†mka bjt egp
kmfrbghi‚) 
                                              v      v
   4◦ . (x1 )2 + (x2 )2 + (x3 )2 ( dbadjt gbasmh jt egkmfrbghi‚) 
                                                   v       v
   5◦ . (x1 )2 + (x2 )2 − (x3 )2 ( kmqmhikmbbjt gbasmh jt egkmfrbghi‚) 
                                                   v u           v
   6◦ . (x1 )2 + (x2 )2 = 0 ( ejfj dbadcr eogh ghim w emfmhm j{qarht eg
kmqmhikmbbgu eftdgu x1 = x2 = 0) 
                                                             v
   7◦ . (x1 )2 − (x2 )2 = 0 ( ejfj kmqmhikmbbcr emfmhm j{qarht eogh gp
                                                                          v
himu) 
                                     n            v u
   8◦ . (x1 )2 = 0 ( ejfj hgkej j{qar eogh ghim ) €
    ªœZœ«œ µÜ^ ’-15“07*  )7- D68 BA+35,,-” .-DC-D8ˆ0: -+35E-: ,*/-+
/7B*,,-” .6-/1-/70 P2 ⊂ P3  )5/7> .-B*3C,-/70 2◦  .30,5D6*“5ˆ58 A3 =
P3 \ P2  :-“*7 -15E57>/8 ¨660./-0D-:  DB2.-6-/7,A: 90.*3+-6-0D-: 060
¨660.70)*/10: .535+-6-0D-:Œ )5/7> .-B*3C,-/70 3◦ F -D,-.-6-/7,A: 90
.*3+-6-0D-: 060 90.*3+-60)*/10: .535+-6-0D-:Œ 5 )5/7> .-B*3C,-/70 5◦
F 1-,2/-: 060 ½060,D3-:<
    5 /6*D2‡ˆ*: 30/2,1* .-15E5,- 7-.-6-90)*/1-* /73-*,0* .-B*3C,-/7*”
2◦  3◦ 0 5◦ <




   2◦                      3◦                      5◦



Ý^–µ £›—°˜š›Y\\—Y WX—Y™š]›\—Y WX—˜šXœ\˜š›— Pn∗ ^
 5//:-730: :,-“*/7B- 90.*3.6-/1-/7*” B .3-/735,/7B* Pn < +-E,5)0: ¨7-
:,-“*/7B- /0:B-6-: Pn∗ < 5“D58 90.*3.6-/1-/7> π ⊂ Pn .3*D/75B68*7 /-
+-” -+35E p(Vn(π))  9D* Vn(π) ⊂ Vn+1 F .-D.3-/735,/7B-  5//-½003-B5,

                                     Ñ©