Kahler Manifold Research Articles

Axionphilic cosmological moduli

We show that string moduli have axion-philic nature owing to the model-insensitive derivative interactions arising from the Kaehler potential. The decay of a modulus into stringy axions occurs without suppression by the mass of final states. Interestingly, it turns out to hold in general not only for the scalar partner of the stringy axion but also for any other moduli. The decay into (pseudo) Nambu-Goldstone bosons (NGBs) also avoids such mass suppression if the modulus is lighter than or similar in mass to the scalar partner of the NGB. Such axion-philic nature makes string moduli a natural source of an observable amount of dark radiation in string compactifications involving ultralight stringy axions, and possibly in extensions of the Standard Model that include a cosmologically stable NGB such as the QCD axion. In the latter case, the fermionic superpartner of the NGB can also contribute to the dark matter as a feebly interacting massive particle.

Geometric Mechanics on Warped Product Semi-Slant Submanifold of Generalized Complex Space Forms

In this study, we develop a general inequality for warped product semi-slant submanifolds of type M n = N T n 1 × f N ϑ n 2 in a nearly Kaehler manifold and generalized complex space forms using the Gauss equation instead of the Codazzi equation. There are several applications that can be developed from this. It is also described how to classify warped product semi-slant submanifolds that satisfy the equality cases of inequalities (determined using boundary conditions). Several results for connected, compact warped product semi-slant submanifolds of nearly Kaehler manifolds are obtained, and they are derived in the context of the Hamiltonian, Dirichlet energy function, gradient Ricci curvature, and nonzero eigenvalue of the Laplacian of the warping functions.

SU(2,1)/(SU(2) × U(1)) B − L Higgs Inflation

We present a realization of Higgs inflation within Supergravity which is largely tied to the existence of a pole of order two in the kinetic term of the inflaton field. This pole arises due to the selected Kaehler potential which parameterizes the SU(2,1)/(SU(2) × U(1)) manifold with scalar curvature . The associated superpotential includes, in addition to the Higgs superfields, a stabilizer superfield, respects a B − L gauge and an R symmetries and contains the first allowed nonrenormalizable term. If the coefficient of this term is almost equal to that of the others within about 10−5 and N = 2, the inflationary observables can be done compatible with the present data. The tuning can be eluded if we modify the Kaehler potential associated with the manifold above. In this case, inflation can be realized with just renormalizable superpotential terms and results to higher tensor-to-scalar ratios as N approaches its maximum at N ≃80.

Geometry of Pointwise Semi-slant Warped Products in Locally Conformal Kaehler Manifolds

In this paper, we study the geometry of pointwise semi-slant warped products in a locally conformal Kaehler manifold. In particular, we obtain several results which extend Chen’s inequality for CR-warped product submanifolds in Kaehler manifolds. Also, we study the corresponding equality cases. Several related results on pointwise semi-slant warped products are also proved in this paper.

Remarks on conformal anti-invariant Riemannian maps to cosymplectic manifolds

M.A. Akyol and B. Şahin [Conformal anti-invariant Riemannian maps to Kaehler manifolds, U.P.B. Sci. Bull., Series A, Vol. 80, Iss. 4, 2018] defined and studied the notion of conformal anti-invariant Riemannian maps to Kaehler manifolds. In this paper, as a generalization of totally real submanifolds and anti-invariant Riemannian maps, we extend this notion to almost contact metric manifolds. In this manner, we introduce conformal anti-invariant Riemannian maps from Riemannian manifolds to cosymplectic manifolds. In order to guarantee the existence of this notion, we give a non-trivial example, investigate the geometry of foliations which are arisen from the definition of a conformal Riemannian map and obtain decomposition theorems by using the existence of conformal Riemannian maps. Moreover, we investigate the harmonicity of such maps and find necessary and sufficient conditions for conformal anti-invariant Riemannian maps to be totally geodesic. Finally, we study weakly umbilical conformal Riemannian maps and obtain a classification theorem for conformal anti-invariant Riemannian maps.

Conformal-twisted product semi-slant submanifolds in globally conformal Kaehler manifolds

We introduce the notion of conformal-twisted product submanifolds of the form $_fM^{T}\times_{b}M^{\theta}$ and $_fM^{\theta}\times_{b}M^{T}$, where $M^T$ is a holomorphic submanifold and $M^\theta$ is a proper slant submanifold of $M$ in a globally conformal Kaehler manifold and $f$ and $b$ are conformal factor and twisting function, respectively. We give necessary and sufficient conditions for proper semi-slant submanifold to be a locally conformal-twisted product for such submanifolds of the form $_fM^{T}\times_{b}M^{\theta}$ and $_fM^{\theta}\times_{b}M^{T}$. We establish a general inequality for the squared norm of second fundamental form of these types of submanifolds.

Homology of contact 3-CR-submanifolds of an almost 3-contact hypersurface

It is well known that a 4n-dimensional Euclidean space has a parallel quaternion Kaehler structure, and the hypersurface of this space has an almost 3-contact metric structure. This article investigates the non-existence of stable integral currents on compact contact 3-CR-submanifold and gives vanishing theorems concerning the homology groups of such submanifolds.

Trans-Sasakian 3-manifolds with Einstein-like Ricci operators

Let M be a trans-Sasakian 3-manifold such that the Ricci curvature of the structure vector field vanishes. In this paper, it is proved that if M is compact, then it is homothetic to a cosymplectic manifold. Without the compactness assumption, we prove that M is locally isometric to the product of ℝ and a Kahler surface of constant curvature if the Ricci operator of M is of Codazzi type or cyclic parallel. We classify trans-Sasakian 3-manifolds with Killing type Ricci tensors. We construct some concrete examples to illustrate the above theorems.

A β-tensor on Kaehler manifolds and its geometric characterizations

In this paper, we first introduce a new notion [Formula: see text]-tensor on Hermitian manifold and particularly, we present some geometric characterizations of such a tensor on the Kaehler manifold. Here, we investigate the Kaehler submersion whose total space is equipped with the [Formula: see text]-tensor and obtain some results. Also, we deal with a Kaehler submersion with totally geodesic fibers such that the total space admits [Formula: see text]-Ricci soliton and [Formula: see text]-tensor. Finally, we give necessary conditions for which any fiber and base manifold of Kaehler submersion is [Formula: see text]-Ricci soliton or [Formula: see text]-Kaehler-Einstein.

Semi-Invariant Riemannian Submersions with Semi-Symmetric Non-Metric Connection

In this paper, we investigate semi-invariant Riemannian submersion from a Kaehler manifold with semi-symmetric non-metric connection to a Riemannian manifold. We study the geometry of foliations with semi-symmetric non-metric connection. Later, we introduce base manifold to be a local product manifold with semi-symmetric non-metric connection.

Nilpotent structures and collapsing Ricci-flat metrics on the K3 surface

We exhibit families of Ricci-flat Kahler metrics on K3 surfaces which collapse to an interval, with Tian-Yau and Taub-NUT metrics occurring as bubbles. There is a corresponding continuous surjective map from the K3 surface to the interval, with regular fibers diffeomorphic to either 3-tori or Heisenberg nilmanifolds.

On deformations of Fano manifolds

In this paper, we provide new necessary and sufficient conditions for the existence of Kahler–Einstein metrics on small deformations of a Fano Kahler–Einstein manifold. We also show that the Weil–Petersson metric can be approximated by the Ricci curvatures of the canonical $$L^2$$ metrics on the direct image bundles. In addition, we describe the plurisubharmonicity of the energy functional of harmonic maps on the Kuranishi space of the deformation of compact Kahler–Einstein manifolds of general type.

The Witten deformation of the Dolbeault complex

We introduce a Witten–Novikov type perturbation $$\bar{\partial }_{\bar{\omega }}$$ of the Dolbeault complex of any complex Kahler manifold, defined by a form $$\omega $$ of type (1, 0) with $$\partial \omega =0$$ . We give an explicit description of the associated index density which shows that it exhibits a nontrivial dependence on $$\omega $$ . The heat invariants of lower order are shown to be zero.

Some remarks on a family of warped product pointwise semi-slant submanifolds of Kaehler manifold

The purpose of this paper is to provide the complete classifications of the second fundamental form inequality for a warped product pointwise semi-slant submanifold in a Kaehler manifold which was obtained by Şahin [Th. 5.2, Warped product pointwise semi-slant submanifold of Kaehler manifold, Port. Math. 2013] in terms of intrinsic and extrinsic invariants. In this paper, we give some conditions that are not addressed or considered in the cited paper mentioned above. Finally, we provide necessary and sufficient conditions that satisfy inequalities' equalities.

Extension of the curvature form of the relative canonical line bundle on families of Calabi–Yau manifolds and applications

Given a proper, open, holomorphic map of Kahler manifolds, whose general fibers are Calabi-Yau manifolds, the volume forms for the Ricci-flat metrics induce a hermitian metric on the relative canonical bundle over the regular locus of the family. We show that the curvature form extends as a closed positive current. Consequently the Weil-Petersson metric extends as a positive current. In the projective case, the Weil-Petersson form is known to be the curvature of a certain determinant line bundle, equipped with a Quillen metric. As an application we get that after blowing up the singular locus, the determinant line bundle extends, and the Quillen metric extends as singular hermitian metric, whose curvature is a positive current.

Horizontality in the twistor spaces associated with vector bundles of rank 4 on tori

Let E be an oriented vector bundle of rank 4 over a torus $$T^2$$ with a metric h and $$\hat{E}$$ the twistor space associated with E. We will study the horizontality in $$\hat{E}$$ with respect to the connection $$\hat{\nabla }$$ induced by an h-connection $$\nabla $$ . We will describe the subset of the fiber $$\hat{E}_a$$ of $$\hat{E}$$ at a point $$a\in T^2$$ given by horizontality along normal polygonal curves in $${{\varvec{R}}}^2$$ for an initial value at a in the case where the subset is finite. We will see that if $$\hat{E}$$ has a partially horizontal section $$\Omega $$ , then there exists an h-connection $$\nabla '$$ related to $$\nabla $$ such that h, $$\nabla '$$ and $$\Omega $$ give a Kahler structure of E. We will make analogous discussions for an oriented vector bundle of rank 4 over $$T^2$$ with a neutral metric.

A KAHLER MANIFOLD ADMITTING SEMI-SYMMETRIC METRIC CONNECTION A.

In present paper we study the properties of Kahler manifold satisfying the semi - symmetric metric connection. Symmetric and skew-symmetric conditions for Nijenhuis tensor of the connection in Kahler manifold has been discussed. The paper also includes some properties of contravariant almost analytic vector field in a Kahler manifold.

The Chern–Ricci flow on primary Hopf surfaces

The Hopf surfaces provide a family of minimal non-Kähler surfaces of class VII on which little is known about the Chern–Ricci flow. We use a construction of Gauduchon–Ornea for locally conformally Kähler metrics on primary Hopf surfaces of class 1 to study solutions of the Chern–Ricci flow. These solutions reach a volume collapsing singularity in finite time, and we show that the metric tensor satisfies a uniform upper bound, supporting the conjecture that the Gromov-Hausdorff limit is isometric to a round\(S^1\). Uniform \(C^{1+\beta }\) estimates are also established for the potential. Previous results had only been known for the simplest examples of Hopf surfaces.

Kahlerian manifolds related in H-projective recurrent curvature killing vector fields with vectorial fields

Izumi and Kazanari [2], has calculated and defined on infinitesimal holomorphically projective transformations in compact Kaehlerian manifolds. Also, Malave Guzman [3], has been studied transformations holomorphic ammeters projective equivalentes. After that, Negi [5], have studied and considered some problems concerning Pseudo-analytic vectors on Pseudo-Kaehlerian Manifolds. Again, Negi, et. al. [6],has defined and obtained an analytic HP-transformation in almost Kaehlerian spaces. In this paper we have measured and calculated a Kahlerian manifolds related in H-projective recurrent curvature killing vector fields with vectorial fields and their holomorphic propertiesEinsteinian and the constant curvature manifoldsare established.Kaehlerian holomorphically projective recurrent curvature manifolds with almost complex structures by using the geometrical properties of the harmonic and scalar curvatures calculated overkilling vectorial fieldsare obtained

On the compactness of Hamiltonian stationary Lagrangian surfaces in Kähler surfaces

We prove a bubble tree convergence theorem for a sequence of closed Hamiltonian stationary Lagrangian surfaces with bounded areas and Willmore energies in a complete Kahler surface. We also prove two strong compactness theorems on the space of Hamiltonian stationary Lagrangian tori in $${\mathbb {C}}^2$$ and $${{\mathbb {C}}}{{\mathbb {P}}}^2$$ respectively.