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126
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 ..."
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Cited by 63 (14 self)
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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 ..."
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Cited by 60 (21 self)
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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.
ALMOST KÄHLER DEFORMATION QUANTIZATION
, 2001
"... Abstract. We use a natural affine connection with nontrivial torsion on an arbitrary almostKähler manifold which respects the almostKähler structure in order to construct a Fedosovtype deformation quantization on this manifold. 1. ..."
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Cited by 23 (1 self)
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Abstract. We use a natural affine connection with nontrivial torsion on an arbitrary almostKähler manifold which respects the almostKähler structure in order to construct a Fedosovtype deformation quantization on this manifold. 1.
Vanishing Theorems and String Backgrounds
, 2000
"... We show various vanishing theorems for the cohomology groups of compact hermitian manifolds for which the Bismut connection has (restricted) holonomy contained in SU(n) and classify all such manifolds of dimension four. In this way we provide necessary conditions for the existence of such structures ..."
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Cited by 23 (1 self)
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We show various vanishing theorems for the cohomology groups of compact hermitian manifolds for which the Bismut connection has (restricted) holonomy contained in SU(n) and classify all such manifolds of dimension four. In this way we provide necessary conditions for the existence of such structures on hermitian manifolds. Then we apply our results to solutions of the string equations and show that such solutions admit various cohomological restrictions like for example that under certain natural assumptions the plurigenera vanish. We also find that under some assumptions the string equations are equivalent to the condition Riemannian manifolds equipped with a closed form have found many applications in various branches of mathematics and physics. In physics, the classical example is that of manifolds equipped with a closed twoform which describe gravity in the presence of a Maxwell field. More recently, Riemannian or pseudoRiemannian manifolds M equipped with (closed) forms
Deformation Quantization of Almost Kähler Models and Lagrange–Finsler Spaces
, 2007
"... Finsler and Lagrange spaces can be equivalently represented as almost Kähler manifolds enabled with a metric compatible canonical distinguished connection structure generalizing the Levi Civita connection. The goal of this paper is to perform a natural Fedosov–type deformation quantization of such g ..."
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Cited by 22 (20 self)
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Finsler and Lagrange spaces can be equivalently represented as almost Kähler manifolds enabled with a metric compatible canonical distinguished connection structure generalizing the Levi Civita connection. The goal of this paper is to perform a natural Fedosov–type deformation quantization of such geometries. All constructions are canonically derived for regular Lagrangians and/or fundamental Finsler functions on tangent bundles.
KT and HKT geometries in strings and black hole moduli spaces
"... Some selected applications of KT and HKT geometries in string theory, supergravity, black hole moduli spaces and hermitian geometry are reviewed. It is shown that the moduli spaces of a large class of fivedimensional supersymmetric black holes are HKT spaces. In hermitian geometry, it is shown that ..."
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Cited by 12 (0 self)
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Some selected applications of KT and HKT geometries in string theory, supergravity, black hole moduli spaces and hermitian geometry are reviewed. It is shown that the moduli spaces of a large class of fivedimensional supersymmetric black holes are HKT spaces. In hermitian geometry, it is shown that a compact, conformally balanced, strong KT manifold whose associated KT connection has holonomy contained in SU(n) is CalabiYau. The implication of this result in the context of some string compactifications is explained
Indefinite almost paracontact metric manifolds
, 2009
"... In this paper we introduce the concept of (ε)almost paracontact manifolds, and in particular, of (ε)para Sasakian manifolds. Several examples are presented. Some typical identities for curvature tensor and Ricci tensor of (ε)para Sasakian manifolds are obtained. We prove that if a semiRiemannia ..."
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Cited by 7 (5 self)
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In this paper we introduce the concept of (ε)almost paracontact manifolds, and in particular, of (ε)para Sasakian manifolds. Several examples are presented. Some typical identities for curvature tensor and Ricci tensor of (ε)para Sasakian manifolds are obtained. We prove that if a semiRiemannian manifold is one of flat, proper recurrent or proper Riccirecurrent, then it can not admit an (ε)para Sasakian structure. We show that, for an (ε)para Sasakian manifold, the conditions of being symmetric, semisymmetric or of constant sectional curvature are all identical. It is shown that a symmetric spacelike (resp. timelike) (ε)para Sasakian manifold Mn is locally isometric to a pseudohyperbolic space Hn ν (1) (resp. pseudosphere Sn ν (1)). In last, it is proved that for an (ε)para Sasakian manifold, the conditions of being Riccisemisymmetric, Riccisymmetric
On Riemannian almost product manifolds with nonintegrable structure
, 2008
"... Abstract. The class of the Riemannian almost product manifolds with nonintegrable structure is considered. Some identities for curvature tensor as certain invariant tensors and quantities are obtained. Mathematics Subject Classification (2000): 53C15, 53C50 Key words: almost product manifold, Rieman ..."
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Cited by 6 (2 self)
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Abstract. The class of the Riemannian almost product manifolds with nonintegrable structure is considered. Some identities for curvature tensor as certain invariant tensors and quantities are obtained. Mathematics Subject Classification (2000): 53C15, 53C50 Key words: almost product manifold, Riemannian metric, nonintegrable structure
The Ricci Curvature of Halfflat Manifolds
, 2006
"... We derive expressions for the Ricci curvature tensor and scalar in terms of intrinsic torsion classes of halfflat manifolds by exploiting the relationship between halfflat manifolds and noncompact G2 holonomy manifolds. Our expressions are tested for Iwasawa and more general nilpotent manifolds. ..."
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Cited by 6 (0 self)
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We derive expressions for the Ricci curvature tensor and scalar in terms of intrinsic torsion classes of halfflat manifolds by exploiting the relationship between halfflat manifolds and noncompact G2 holonomy manifolds. Our expressions are tested for Iwasawa and more general nilpotent manifolds. We also derive expressions, in the language of CalabiYau moduli spaces, for the torsion classes and the Ricci curvature of the particular halfflat manifolds that arise naturally via mirror symmetry in flux compactifications. Using these expressions we then derive a constraint on the Kähler moduli space of type II string theory on these halfflat manifolds.