In our paper "Existence of Extremal Metrics on Almost Homogeneous
Manifolds of Cohomogeneity One" we gave a proof of the existence of
K\"ahler-Einstein metrics on $M_{n}$ the blow-up of
$CP^{n}\times CP^{n}$ along the diagonal by
conidering the Ricci class and the symmetric Ricci curvature
equation.
In this paper we consider the general K\"ahler
classes and the scalar curvature equations
as it was in my earier paper
"Existence of Extremal Metrics on Almost Homogeneous
Spaces with Two Ends". New feature appears in this paper.
We can prove the existence for a K\"ahler class with which
certain integral is negative. We expect that if the
considered integral is nonnegative then there is no 
extremal metric in the considered K\"ahler class. This is 
suggested from the generalized Futaki invariants constructed by
Ding and Tian. Therefore, our result can be considered
as examples of the converse of Tian's observation
on the weakly K-stability. 
We also give a complete proof for the existence
of constant scalar curvature on almost homogeneous
manifolds with two <b>hypersurface</b> ends and with
reductive automorphism group, which we
need in this paper. 
We shall consider
the manifolds $N_{n}=M_{n}/S_{2}$ in the
third paper.(Abstract posted on Dec. 7, 1998) 
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1991 Mathematics Subject Classification: 32M12, 53C25, 14M20,
14J45, 32L07