四川大学2008年微分几何考博试题.pdf
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1. f : R2 3 2 3 R2
R f (u v) (uv u u v), , X 2v u v
2 2 3
xy dx x ydy zdz R
(1): f (X ), f ()
(2): f
(3) C
C
˜
2. D, D n M
˜
(1):D D M (1,2) .
(2): f M f i j f D f i j f ji
3. (M G) n
l k l k
(1): X M Ri jkX 0, Ri jk , X
k
X
(2): Ricci R R fG f M M
4. M n M n
0
M
¯T 1
5. S U (n) A GL(n C)A A det(A) 1 n
(1):.
(2): X , X S U (n)
6. [z z z ] nCPn
0 1 n
n
1 2 n
¯
(1):2 log z CP (1,1)
2 i
i0
n n
¯ n
dz dz¯ , CP HermiteKahler
zi i z¯i i
i0 i0
(2): ()
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