Тригонометрия гиперболической плоскости положительной кривизны. Ромакина Л.Н. - 51 стр.

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a πρ/2 B
p
˜a ˜a > πρ/2 a < πρ/2) D
˜a
(BCB
p
D) = 2
b
2
3
1
2b
3
c
3
1
.
(BCB
p
D) 2b
3
c
3
1
˜a > πρ/2 2b
3
c
3
1 < 0, ˜a < πρ/2 2b
3
c
3
1 > 0.
= 1
B a
c
ch B = δi
2c
3
b
3
p
4c
3
(b
3
c
3
) 1
, δ = ±1.
δ
B a
0
a
A
0
= a
0
AA
2
A
0
AA
2
B a
0
B A
0
AD
B =
πi
2
+ ϕ (ADA
0
A
2
) > 0, B =
πi
2
(ADA
0
A
2
) = 0,
B =
πi
2
ϕ (ADA
0
A
2
) < 0, ϕ R
+
.
(ADA
0
A
2
)
ˆ
H
A
2
A
R a
0
(1 2b
3
c
3
: 2b
2
3
2b
3
c
3
1 : 2(2c
3
b
3
)) A
0
(0 : 2(b
3
2c
3
) :
2b
2
3
2b
3
c
3
1)
(ADA
0
A
2
) =
2(b
3
c
3
)(2c
3
b
3
)
4c
3
(b
3
c
3
) 1
.
(ADA
0
A
2
)
(b
3
c
3
)(2c
3
b
3
) b
3
> c
3
A
(c
3
b
3
: c
3
: 0) a
ˆ
H E
12
A
E
12
A
1
A
2
(A
E
12
A
1
A
2
) =
c
3
b
3
c
3
< 0.
b
3
> c
3
(ADA
0
A
2
) 2c
3
b
3
δ = 1
= δ = 1