 
Summary: Journal of Algebra 269 (2003) 480491
www.elsevier.com/locate/jalgebra
Quasipotentials and KählerEinstein metrics
on flag manifolds, II
Hassan Azad a,
and Indranil Biswas b
a Department of Mathematical Sciences, King Fahd University, Dhahran 31261, Saudi Arabia
b School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
Received 5 May 2002
Communicated by J.T. Stafford
Abstract
For a homogeneous space G/P, where P is a parabolic subgroup of a complex semisimple
group G, an explicit KählerEinstein metric on it is constructed. The Einstein constant for the metric
is 1. Therefore, the intersection number of the first Chern class of the holomorphic tangent bundle of
G/P coincides with the volume of G/P with respect to this KählerEinstein metric, thus enabling
us to compute volume for this metric and for all Kählerian metrics on G/P invariant under the action
of a maximal compact subgroup of G.
2003 Elsevier Inc. All rights reserved.
1. Introduction
Let G be a complex reductive group, P a parabolic subgroup of G and K a maximal
