Abstract
AbstractWe study some types of qc-Einstein manifolds with zero qc-scalar curvature introduced by S. Ivanov and D. Vassilev. Secondly, we shall construct a family of quaternionic Hermitian metrics $$(g_a,\{J_\alpha \}_{\alpha =1}^3)$$
(
g
a
,
{
J
α
}
α
=
1
3
)
on the domain Y of the standard quaternion space $${\mathbb {H}}^n$$
H
n
one of which, say $$(g_a,J_1)$$
(
g
a
,
J
1
)
is a Bochner flat Kähler metric. To do so, we deform conformally the standard quaternionic contact structure on the domain X of the quaternionic Heisenberg Lie group$${{\mathcal {M}}}$$
M
to obtain quaternionic Hermitian metrics on the quotient Y of X by $${\mathbb {R}}^3$$
R
3
.
Funder
Japan Society for the Promotion of Science
Publisher
Springer Science and Business Media LLC
Subject
Geometry and Topology,Analysis