Vanishing theorems and string backgrounds

@article{Ivanov2000VanishingTA,
  title={Vanishing theorems and string backgrounds},
  author={Stefan Ivanov and Georgios Papadopoulos},
  journal={Classical and Quantum Gravity},
  year={2000},
  volume={18},
  pages={1089-1110}
}
We show various vanishing theorems for the cohomology groups of compact Hermitian manifolds for which the Bismut connection has a (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 compact Hermitian manifolds with vanishing first Chern class of non-Kahler type. Then we apply our results to solutions of the string equations and show that such solutions admit various… 

Deformations of generalized calibrations and compact non-Kähler manifolds with vanishing first Chern class

We investigate the deformation theory of a class of generalized calibrations in Riemannian manifolds for which the tangent bundle has reduced structure group U(n), SU(n), G_2 and Spin(7). For this we

Non-Kähler Calabi-Yau manifolds

We study the class of compact complex manifolds whose first Chern class vanishes in the Bott-Chern cohomology. This class includes all manifolds with torsion canonical bundle, but it is strictly

Index theorems on torsional geometries

We investigate the Atiyah-Singer index theorems with torsion given by Neveu-Schwarz three-form flux H under the condition dH = 0 in flux compactification scenarios with non-trivial background fields

Generalised G2–Manifolds

We define new Riemannian structures on 7–manifolds by a differential form of mixed degree which is the critical point of a (possibly constrained) variational problem over a fixed cohomology class.

Non-K\"ahler Calabi-Yau manifolds

We study the class of compact complex manifolds whose first Chern class vanishes in the Bott-Chern cohomology. This class includes all manifolds with torsion canonical bundle, but it is strictly

Vanishing theorems for locally conformal hyperkaehler manifolds

Let M be a compact locally conformal hyperkaehler manifold. We prove a version of Kodaira-Nakano vanishing theorem for M. This is used to show that M admits no holomorphic differential forms, and the

NON-KÄHLER MANIFOLDS WITH SU ( 3 ) STRUCTURE

For a given complex n-fold M we present an explicit construction of all complex (n + 1)-folds which are principal holomorphic T 2-fibrations over M . For physical applications we consider the case of

GENERALIZED RICCI FLOW AND SUPERGRAVITY VACUUM SOLUTIONS

We first give a proof that the supersymmetric configurations satisfy the equations of motion for type II supergravity. In flux compactifications, the string vacua preserving N = 2 supersymmetry are

Geometric Model for Complex Non-Kähler Manifolds with SU (3) Structure

For a given complex n-fold M we present an explicit construction of all complex (n+1)-folds which are principal holomorphic T2-fibrations over M. For physical applications we consider the case of M
...

References

SHOWING 1-10 OF 55 REFERENCES

Vanishing theorems on Hermitian manifolds

Geometry of quaternionic Kähler connections with torsion

Complex structures on quaternionic manifolds

Curvature properties of twistor spaces of quaternionic Kähler manifolds

We present a study of natural almost Hermitian structures on twistor spaces of quaternionic Kahler manifolds. This is used to supply (4n + 2)-dimensional examples (n > 1) of symplec tic non-Kähler

Geometry of Hyper-Kähler Connections with Torsion

Abstract:The internal space of a N = 4 supersymmetric model with Wess–Zumino term has a connection with totally skew-symmetric torsion and holonomy in SP(n). We study the mathematical background of
...