arXiv research

Constructs non-Kähler Calabi-Yau 3-folds with large Betti numbers.

Study shows continuity of non-Kähler Calabi-Yau conifold transitions.

Constructs special Lagrangian 3-spheres in non-Kähler compact threefolds.

Constructs non-Kähler Calabi-Yau manifolds with large Betti numbers.

New metrics found on non-Kähler Calabi-Yau manifolds.

Study finds isolated SL submanifolds on non-Kähler Calabi-Yau threefolds.

Lecture notes on non-Kähler complex threefolds, focusing on conifold transitions.

Study on non-Kähler Calabi-Yau manifolds and their geometric structures.

We construct balanced metrics on the family of non-Kähler Calabi-Yau threefolds that are obtained by smoothing after contracting $(-1,-1)$-rational curves on Kähler Calabi-Yau threefold. As an application, we construct balanced metrics on complex manifolds diffeomorphic to connected sum of $k\geq 2$ copies of $S^3\time…

Identifies special Lagrangian submanifolds in non-Kähler Calabi-Yau manifolds.

Study on non-Kähler Calabi-Yau geometries on 3-folds with constraints.

New metrics found on non-Kähler Calabi-Yau manifolds.

Study stability of non-Kähler Calabi-Yau metrics using critical points of generalized Einstein Hilbert action.

In arXiv:1008.1018 it is shown that a given stable vector bundle $V$ on a Calabi-Yau threefold $X$ which satisfies $c_2(X)=c_2(V)$ can be deformed to a solution of the Strominger system and the equations of motion of heterotic string theory. In this note we extend this result to the polystable case and construct explic…

We propose a new construction of compact non-Kähler Calabi-Yau manifolds with balanced metrics and study the Strominger system on them. In particular, we obtain explicit solutions to the Strominger system with degeneracies on $Σ_g\times T^4$, where $Σ_g$ is an immersed minimal surface of genus $g\geq3$ in $T^3$.

New metrics found on non-Kähler complex manifolds.

Survey on Strominger system and Ricci flow in non-Kähler geometry.

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 larger. After making some elementary remarks, we show that a manifold in Fujiki's class C with vanishing first Bott-Chern cla…

In this paper, we construct simply connected symplectic Calabi-Yau 6-manifolds by applying Gompf's symplectic fiber sum operation along $T^4$. Using our construction, we also produce symplectic non-Kähler Calabi-Yau 6-manifolds with fundamental group $\Z$. In this paper, we also produce the first examples of simply con…

Study properties of holomorphic $p$-contact manifolds, including non-Kähler hyperbolicity and deformations.

Constructs higher-dimensional twistor spaces for complex manifolds.

We show that supersymmetric M-theory compactifications to three-dimensional Minkowski space-time preserving $\mathcal{N}=2$ supersymmetry allow for a class of internal manifolds more general than the Calabi-Yau one, namely the class of locally conformally Kähler manifolds which locally carry a preferred Calabi-Yau stru…

New metrics solve complex equations on special 3D shapes.

Flow stabilizes on non-Kähler metrics near Calabi-Yau.

We construct a geometric model of eight-dimensional manifolds and realize them in the context of type II string theory. These eight-manifolds are constructed by non-trivial $T^{4}$ fibrations over Calabi-Yau two-folds. These give rise to eight-dimensional non-Kahler Hermitian manifolds with $SU(4)$ structure. The eight…

Study of Hermitian structures on toric suspensions of balanced manifolds.

Study Bismut-Griffiths-positivity in non-Kähler manifolds under Hermitian curvature flows.

The connection between Hitchin's stable forms and vector cross products is observed. Using this correspondence, we construct new examples of non-Kahler Calabi-Yau 3-folds and manifolds with G2-structure of class W3. We also generalize and refine results of Calabi and Gray in the paracomplex setting.

Study of $t$-Gauduchon Ricci-flat condition under Chern-Ricci flow on non-Kähler manifolds.

We study a supersymmetry-preserving solution-generating method in heterotic supergravity. In particular, we use this method to construct one-parameter non-Kahler deformations of Calabi-Yau manifolds with a U(1) isometry, in which the complex structure remains invariant. We explain how to obtain corresponding solutions …

Paper finds infinitely many smooth solutions to complex geometry problem.

This work extends Yau's theorem to non-Kähler manifolds using holomorphic Courant algebroids.

We show existence of unique smooth solutions to the Monge-Ampere equation for (n-1)-plurisubharmonic functions on Hermitian manifolds, generalizing previous work of the authors. As a consequence we obtain Calabi-Yau theorems for Gauduchon and strongly Gauduchon metrics on a class of non-Kahler manifolds: those satisfyi…

New non-Kähler 3-folds constructed via log conifold transitions.

We propose a construction of Kähler and non-Kähler Calabi-Yau manifolds by branched double covers of twistor spaces. In this construction we use the twistor spaces of four-manifolds with self-dual conformal structures, with the examples of connected sum of $n$ $\mathbb{P}^{2}$s. We also construct $K3$-fibered Calabi-Ya…

The paper describes Hermitian non-Kähler structures on complex flag manifolds.

Given a compact complex $n$-fold $X$ satisfying the $\partial\bar\partial$-lemma and supposed to have a trivial canonical bundle $K_X$ and to admit a balanced (=semi-Kähler) Hermitian metric $ω$, we introduce the concept of deformations of $X$ that are {\bf co-polarised} by the balanced class $[ω^{n-1}]\in H^{n-1,\,n-1…

We construct a class of stable SU(5) bundles on an elliptically fibered Calabi-Yau threefold with two sections, a variant of the ordinary Weierstrass fibration, which admits a free involution. The bundles are invariant under the involution, solve the topological constraint imposed by the heterotic anomaly equation and …

Our aim here is to investigate the holomorphic geometric structures on compact complex manifolds which may not be Kähler. We prove that holomorphic geometric structures of affine type on compact Calabi-Yau manifolds with polystable tangent bundle (with respect to some Gauduchon metric on it) are locally homogeneous. In…

The paper constructs flat metrics on orbifolds and resolutions.

We prove that the non-Kahler locus of a nef and big class on a compact complex manifold bimeromorphic to a Kahler manifold equals its null locus. In particular this gives an analytic proof of a theorem of Nakamaye and Ein-Lazarsfeld-Mustata-Nakamaye-Popa. As an application, we show that finite time non-collapsing singu…

Classifies non-Kahler surfaces and proves local conformal Kahler property.

Study cohomological and metric properties of non-Kähler complex manifolds.

In this article, we examine the behavior of the Riemannian and Hermitian curvature tensors of a Hermitian metric, when one of the curvature tensors obeys all the symmetry conditions of the curvature tensor of a Kähler metric. We will call such metrics G-Kähler-like or Kähler-like, for lack of better terminologies. Such…

Proves Liouville theorem for non-Kähler manifolds.

The abstract discusses how generalized Calabi-Gray manifolds help solve non-Kähler geometry questions.

Study examines flow behavior on non-Kähler manifolds.

Study connects Kähler and non-Kähler hyperbolicity.