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Рубрика:
d = 2 N = 3 E = R
2
ϕ :
(
x = 0
y = u
z = v
.
ϕ
0
rang ϕ
0
= 2
ϕ
yz
A ⊂ R
d
B ⊂ R
N
ϕ A
B
ϕ ∈ C
(1)
(A) ψ ∈ C
(1)
(B)
ψ|
B
= ϕ
−1
ϕ : E −→ S
S ϕ
ϕ
ϕ ∈ C
(1)
(E)
ϕ
−1
S
C
(1)
(S) x
0
= (x
0
1
, . . . , x
0
N
) ∈ S
t
0
= (t
0
1
, . . . , t
0
d
) = ϕ
−1
(x
0
) rang ϕ
0
(t
0
) = d
k
1
, . . . , k
d
¯
¯
¯
¯
¯
¯
¯
∂ϕ
k
1
∂t
1
(t
0
) . . .
∂ϕ
k
1
∂t
d
(t
0
)
∂ϕ
k
d
∂t
1
(t
0
) . . .
∂ϕ
k
d
∂t
d
(t
0
).
¯
¯
¯
¯
¯
¯
¯
6= 0.
k
l
= l l = 1, . . . , d
x = (x
1
, . . . , x
N
)
d x
1
, . . . , x
d
ex ex
0
= (x
0
1
, . . . , x
0
d
)
ϕ
k
(t) = u
k
, k = 1, . . . , d,
