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24
The Existence of Supersymmetric String Theory with Torsion
, 2005
"... ... Strominger and Witten took the matric product of a maximal symmetric four dimensional spacetime M with a six dimensional Calabi–Yau vacua X as the ten dimensional spacetime; they identified the Yang–Mills connection with the SU(3) connection of the Calabi– Yau metric and set the dilaton to be a ..."
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Cited by 51 (5 self)
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... Strominger and Witten took the matric product of a maximal symmetric four dimensional spacetime M with a six dimensional Calabi–Yau vacua X as the ten dimensional spacetime; they identified the Yang–Mills connection with the SU(3) connection of the Calabi– Yau metric and set the dilaton to be a constant. To make this theory compatible with the standard grand unified field theory, Witten [28] and Horava–Witten [20] proposed to use higher rank bundles for strong coupled heterotic string theory so that the gauge groups can be SU(4) or SU(5). Mathematically, this approach relies on Uhlenbeck–Yau’s theorem on constructing Hermitian–Yang–Mills connections on stable bundles [27]. Many authors, including Friedman, Morgan and Witten [18]; Donagi, Ovrat, Pantev and Reinbacher [12]; Andreas [1], Kachru [21] and others, have worked on this subject since then. In [24], Strominger analyzed heterotic superstring background with spacetime sypersymmetry and nonzero torsion by allowing a scalar “warp factor ” to multiply the spacetime metric. He considered a ten dimensional spacetime that is the product M ×X of a maximal symmetric four dimensional spacetime M and an internal space X; themetricon M × X takes the form e 2D(y) � gij(y) 0 0 gµν(x), x ∈ X, y ∈ M; the connection on an auxiliary bundle is Hermitian–Yang–Mills over X:
Almost Hermitian 6manifolds revisited
 J. Geom. Phys
"... Abstract. A Theorem of Kirichenko states that the torsion 3form of the characteristic connection of a nearly Kähler manifold is parallel. On the other side, any almost hermitian manifold of type G1 admits a unique connection with totally skew symmetric torsion. In dimension six, we generalize Kiric ..."
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Cited by 24 (2 self)
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Abstract. A Theorem of Kirichenko states that the torsion 3form of the characteristic connection of a nearly Kähler manifold is parallel. On the other side, any almost hermitian manifold of type G1 admits a unique connection with totally skew symmetric torsion. In dimension six, we generalize Kirichenko’s Theorem and we describe almost hermitian G1manifolds with parallel torsion form. In particular, among them there are only two types ofW3manifolds with a nonabelian holonomy group, namely twistor spaces of 4dimensional selfdual Einstein manifolds and the invariant hermitian structure on the Lie group SL(2, C). Moreover, we classify all naturally reductive hermitianW3manifolds with small isotropy group of the characteristic torsion.
Constructing Balanced metrics on some families of nonKähler Calabi–Yau threefolds, arXiv:0809.4748v1 [math.DG
"... Abstract. We construct balanced metrics on the family of nonKähler CalabiYau threefolds that are obtained by smoothing after contracting (−1, −1)rational curves on Kähler CalabiYau threefold. As an application, we construct balanced metrics on complex manifolds diffeomorphic to connected sum of ..."
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Cited by 12 (2 self)
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Abstract. We construct balanced metrics on the family of nonKähler CalabiYau threefolds that are obtained by smoothing after contracting (−1, −1)rational curves on Kähler CalabiYau threefold. As an application, we construct balanced metrics on complex manifolds diffeomorphic to connected sum of k ≥ 2 copies of S 3 × S 3. 1.
Generalized Kähler manifolds with split tangent bundle
, 2006
"... Abstract. We study generalized Kähler manifolds for which the corresponding complex structures commute and classify completely the compact generalized Kähler fourmanifolds for which the induced complex structures yield opposite orientations. 1. ..."
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Cited by 9 (0 self)
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Abstract. We study generalized Kähler manifolds for which the corresponding complex structures commute and classify completely the compact generalized Kähler fourmanifolds for which the induced complex structures yield opposite orientations. 1.
Curvature of (special) almost Hermitian manifolds
, 2005
"... We study the curvature of almost Hermitian manifolds and their special analogues via intrinsic torsion and representation theory. By deriving different forumlæ for the skewsymmetric part of the ∗Ricci curvature, we find that some of these contributions are dependent on the approach used, and for ..."
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Cited by 8 (3 self)
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We study the curvature of almost Hermitian manifolds and their special analogues via intrinsic torsion and representation theory. By deriving different forumlæ for the skewsymmetric part of the ∗Ricci curvature, we find that some of these contributions are dependent on the approach used, and for the almost Hermitian case we obtain tables that differ from those of Falcitelli, Farinola & Salamon. We show how the exterior algebra may used to explain some of these variations.
On asthenoKähler metrics
"... Abstract. A Hermitian metric on a complex manifold of complex dimension n is called asthenoKähler if its fundamental 2form F satisfies the condition ∂∂F n−2 = 0 and it is strong KT if F is ∂∂closed. We prove that a conformally balanced asthenoKähler metric on a compact manifod of complex dimensi ..."
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Cited by 8 (1 self)
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Abstract. A Hermitian metric on a complex manifold of complex dimension n is called asthenoKähler if its fundamental 2form F satisfies the condition ∂∂F n−2 = 0 and it is strong KT if F is ∂∂closed. We prove that a conformally balanced asthenoKähler metric on a compact manifod of complex dimension n ≥ 3, whose Bismut connection has (restricted) holonomy contained in SU(n), is necessarily Kähler. We provide compact examples of locally conformally balanced asthenoKähler manifolds of complex dimension 3 for which the trace of R B ∧R B vanishes, where R B is the curvature of their Bismut connection. We study blowups of asthenoKähler manifolds for which ∂∂F = 0 and ∂∂F 2 = 0 and we apply these results to orbifolds. Finally, we construct a family of asthenoKähler 2step nilmanifolds of complex dimension 4, showing that, in general, for n> 3, there is no relation between the asthenoKähler and strong KT condition. 1.
NONKÄHLER SOLVMANIFOLDS WITH GENERALIZED KÄHLER STRUCTURE
, 2008
"... Abstract. We construct a compact 6dimensional solvmanifold endowed with a nontrivial invariant generalized Kähler structure and which does not admit any Kähler metric. This is in contrast with the case of nilmanifolds which cannot admit any invariant generalized Kähler structure unless they are to ..."
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Abstract. We construct a compact 6dimensional solvmanifold endowed with a nontrivial invariant generalized Kähler structure and which does not admit any Kähler metric. This is in contrast with the case of nilmanifolds which cannot admit any invariant generalized Kähler structure unless they are tori. 1.