Results 1  10
of
96
Families of strong KT structures in six dimensons
 Comment. Math. Helv
"... Abstract. This paper classifies Hermitian structures on 6dimensional nilmanifolds M = Γ\G for which the fundamental 2form is ∂∂closed, a condition that is shown to depend only on the underlying complex structure J of M. The space of such J is described when G is the complex Heisenberg group, and ..."
Abstract

Cited by 63 (14 self)
 Add to MetaCart
(Show Context)
Abstract. This paper classifies Hermitian structures on 6dimensional nilmanifolds M = Γ\G for which the fundamental 2form is ∂∂closed, a condition that is shown to depend only on the underlying complex structure J of M. The space of such J is described when G is the complex Heisenberg group, and explicit solutions are obtained from a limaçonshaped curve in the complex plane. Related theory is used to provide examples of various types of Ricciflat structures.
A nogo theorem for string warped compactifications
, 2000
"... We give necessary conditions for the existence of perturbative heterotic and type II string warped compactifications preserving eight and four supersymmetries to four spacetime dimensions, respectively. In particular, we find that the only compactifications of heterotic string with the spin connecti ..."
Abstract

Cited by 60 (21 self)
 Add to MetaCart
We give necessary conditions for the existence of perturbative heterotic and type II string warped compactifications preserving eight and four supersymmetries to four spacetime dimensions, respectively. In particular, we find that the only compactifications of heterotic string with the spin connection embedded in the gauge connection and type II strings are those on CalabiYau manifolds with constant dilaton. We obtain similar results for compactifications to six and to two dimensions.
EinsteinWeyl Geometry
 Adv. Math
, 1998
"... instein manifolds with positive scalar curvature and continuous isometries are known to have Einstein deformations, yet we shall see that it is precisely under these two conditions that nontrivial EinsteinWeyl deformations can be shown to exist, at least innitesimally. The EinsteinWeyl condition i ..."
Abstract

Cited by 50 (5 self)
 Add to MetaCart
instein manifolds with positive scalar curvature and continuous isometries are known to have Einstein deformations, yet we shall see that it is precisely under these two conditions that nontrivial EinsteinWeyl deformations can be shown to exist, at least innitesimally. The EinsteinWeyl condition is particularly interesting in three dimensions, where the only Einstein manifolds are the spaces of constant curvature. In contrast, three dimensional EinsteinWeyl geometry is extremely rich [16, 68, 72], and has an equivalent formulation in twistor theory [34] which provides a tool for constructing selfdual four dimensional geometries. In section 10, we shall discuss a construction relating EinsteinWeyl 3manifolds and hyperKahler 4manifolds [40, 29, 50, 79]. Twistor methods also yield complete selfdual Einstein metrics of negative scalar curvature with prescribed conformal innity [48, 35]. An important special case of t
Killing Spinor Equations In Dimension 7 And Geometry Of Integrable G_2Manifolds
, 2008
"... We compute the scalar curvature of 7dimensional G2manifolds admitting a connection with totally skewsymmetric torsion. We prove the formula for the general solution of the Killing spinor equation and express the Riemannian scalar curvature of the solution in terms of the dilation function and the ..."
Abstract

Cited by 41 (0 self)
 Add to MetaCart
We compute the scalar curvature of 7dimensional G2manifolds admitting a connection with totally skewsymmetric torsion. We prove the formula for the general solution of the Killing spinor equation and express the Riemannian scalar curvature of the solution in terms of the dilation function and the NS 3form field. In dimension n = 7 the dilation function involved in the second fermionic string equation has an interpretation as a conformal change of the underlying integrable G2structure into a cocalibrated one of pure type W3.
Selfdual spaces with complex structures, Einstein–Weyl geometry and geodesics
 Ann. Inst. Fourier
"... Abstract. We study the Jones and Tod correspondence between selfdual conformal 4manifolds with a conformal vector field and abelian monopoles on EinsteinWeyl 3manifolds, and prove that invariant complex structures correspond to shearfree geodesic congruences. Such congruences exist in abundance ..."
Abstract

Cited by 33 (7 self)
 Add to MetaCart
(Show Context)
Abstract. We study the Jones and Tod correspondence between selfdual conformal 4manifolds with a conformal vector field and abelian monopoles on EinsteinWeyl 3manifolds, and prove that invariant complex structures correspond to shearfree geodesic congruences. Such congruences exist in abundance and so provide a tool for constructing interesting selfdual geometries with symmetry, unifying the theories of scalarflat Kähler metrics and hypercomplex structures with symmetry. We also show that in the presence of such a congruence, the EinsteinWeyl equation is equivalent to a pair of coupled monopole equations, and we solve these equations in a special case. The new EinsteinWeyl spaces, which we call EinsteinWeyl “with a geodesic symmetry”, give rise to hypercomplex structures with two commuting triholomorphic vector fields. 1.
Structure theorem for compact Vaisman manifolds
, 2003
"... A locally conformally Kähler (l.c.K.) manifold is a complex manifold admitting a Kähler covering ˜ M, with each deck ..."
Abstract

Cited by 29 (19 self)
 Add to MetaCart
A locally conformally Kähler (l.c.K.) manifold is a complex manifold admitting a Kähler covering ˜ M, with each deck
Estimates for the complex MongeAmpère equation on Hermitian and balanced manifolds
, 2009
"... We generalize Yau’s estimates for the complex MongeAmpère equation on compact manifolds in the case when the background metric is no longer Kähler. We prove C ∞ a priori estimates for a solution of the complex MongeAmpère equation when the background metric is Hermitian (in complex dimension two) ..."
Abstract

Cited by 27 (3 self)
 Add to MetaCart
We generalize Yau’s estimates for the complex MongeAmpère equation on compact manifolds in the case when the background metric is no longer Kähler. We prove C ∞ a priori estimates for a solution of the complex MongeAmpère equation when the background metric is Hermitian (in complex dimension two) or balanced (in higher dimensions), giving an alternative proof of a theorem of Cherrier. We relate this to recent results of GuanLi.
Vanishing theorems on Hermitian manifolds
, 2003
"... We prove the vanishing of the Dolbeault cohomology groups on Hermitian manifolds with ddcharmonic Kähler form and positive (1, 1)part of the Ricci form of the Bismut connection. This implies the vanishing of the Dolbeault cohomology groups on complex surfaces which admit a conformal class of Herm ..."
Abstract

Cited by 25 (7 self)
 Add to MetaCart
We prove the vanishing of the Dolbeault cohomology groups on Hermitian manifolds with ddcharmonic Kähler form and positive (1, 1)part of the Ricci form of the Bismut connection. This implies the vanishing of the Dolbeault cohomology groups on complex surfaces which admit a conformal class of Hermitian metrics, such that the Ricci tensor of the canonical Weyl structure is positive. As a corollary we obtain that any such surface must be rational with c2 1> 0. As an application, the pth Dolbeault cohomology groups of a leftinvariant complex structure compatible with a biinvariant metric on a compact even dimensional Lie group are computed.
CalabiYau connections with torsion on toric bundles
"... We find sufficient conditions for principal toric bundles over compact Kähler manifolds to admit CalabiYau connections with torsion, as well as conditions to admit strong Kähler connections with torsion. With the aid of a topological classification, we construct such geometry on (k −1)(S 2 ×S 4)#k( ..."
Abstract

Cited by 24 (0 self)
 Add to MetaCart
(Show Context)
We find sufficient conditions for principal toric bundles over compact Kähler manifolds to admit CalabiYau connections with torsion, as well as conditions to admit strong Kähler connections with torsion. With the aid of a topological classification, we construct such geometry on (k −1)(S 2 ×S 4)#k(S 3 ×S 3) for all k ≥ 1. 1.