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Question: how to calculate the calabi yau threefold's metric's ricci is flat

Question:how to calculate the calabi yau threefold's metric's ricci is flat

ComputerUser 535 Maple 2015
ricci
July 03 2016
0

n := 5:
z1 := exp(2*3.14*I*k1/n)*cosh(z)^(2/n);
z2 := exp(2*3.14*I*k2/n)*sinh(z)^(2/n);
xx := Re(z1);
yy := Re(z2);
uu := cos(alpha)*Im(z1) + sin(alpha)*Im(z2);

use above example of calabi yau equation, do not know which variables z, k1, k2 are u and v, then i assume k1 and k2 are u and v respectively,

 

E := diff(xx,k1).diff(xx,k1);
F := diff(xx,k1).diff(xx,k2);
G := diff(xx,k2).diff(xx,k2);

then calculate metric
diff(E, k2);
F
diff(G, k1);

which function can input these metric diff(E,k2), F, diff(G,k1) to prove calabi yau equation's metric's ricci is flat
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