Kahler Manifold Research Articles

Screen transversal lightlike submersions

In this article, we introduce a new class of lightlike submersions, namely, screen transversal lightlike submersions from an indefinite Kaehler manifold onto a lightlike manifold. This class includes radical screen transversal and screen transversal anti-invariant lightlike submersions as particular cases. We also study some properties of these submersions.

Characterizations of Riemannian maps between Kaehler manifolds by certain curves

Characterizations of Riemannian maps between Kaehler manifolds by certain curves

Semi-Symmetric Metric Connections and Homology of CR-Warped Product Submanifolds in a Complex Space Form Admitting a Concurrent Vector Field

In this paper, we conduct a thorough study of CR-warped product submanifolds in a Kaehler manifold, utilizing a semi-symmetric metric connection within the framework of warped product geometry. Our analysis yields fundamental and noteworthy results that illuminate the characteristics of these submanifolds. Additionally, we investigate the implications of our findings on the homology of these submanifolds, offering insights into their topological properties. Notably, we present a compelling proof demonstrating that, under a specific condition, stable currents cannot exist for these warped product submanifolds. Our research outcomes contribute significant knowledge concerning the stability and behavior of CR-warped product submanifolds equipped with a semi-symmetric metric connection. Furthermore, this work establishes a robust groundwork for future explorations and advancements in this particular field of study.

On the tangent bundles over F-Kahlerian manifolds

The main purpose of the present paper is to study all forms of Riemannien curvatures and the harmonic Killing vector fields of a tangent bundle over an F−Kahlerian manifold endowed with a Berger type deformed Sasaki metric gBS .

PeV-Scale SUSY and Cosmic Strings from F-Term Hybrid Inflation

We consider F-term hybrid inflation (FHI) and SUSY breaking in the context of a B−L extension of the MSSM that largely respects a global U(1)R symmetry. The hidden sector Kaehler manifold enjoys an enhanced SU(1,1)/U(1) symmetry, with the scalar curvature determined by the achievement of a SUSY-breaking de Sitter vacuum without undesirable tuning. FHI turns out to be consistent with the data, provided that the magnitude of the emergent soft tadpole term is confined to the range (1.2–100) TeV, and it is accompanied by the production of B−L cosmic strings. If these are metastable, they are consistent with the present observations from PTA experiments on the stochastic background of gravitational waves with dimensionless tension Gμcs≃(1−9.2)·10−8. The μ parameter of the MSSM arises by appropriately adapting the Giudice–Masiero mechanism and facilitates the out-of-equilibrium decay of the R saxion at a reheat temperature lower than about 71 GeV. Due to the prolonged matter-dominated era, the gravitational wave signal is suppressed at high frequencies. The SUSY mass scale turns out to lie in the PeV region.

Riemannian Maps From Kaehler Manifold With Generic Fibers

We study Riemannian maps from almost Hermitian manifolds to Riemannian manifolds for the case when the fibers are genericsubmanifold of the total space. We obtain the integrability conditionsfor the distributions while vertical distribution is always integrable. Wealso study the geometry of the leaves of the distribution which arisefrom such maps, and obtain the necessary and sufficient conditions forthe fibers as well as the total manifold to be generic product manifolds. We, further, obtain the necessary and sufficient condition for aRiemannian maps with generic fibers to be totally geodesic map.

Projective Tensor of Almost Kahler Manifold

The work from this search is analyze the geometrical characteristics of conharmonic tensor of projectine Almost kahler menifold. we use the projective curvature tensor's flatness properties to determine the projective tensor's Almost kahler manifold compounds. (AK-manifold). And found some components Projective of Almost Kahler. proved that the manifold M is a flat holomorphic sectional tensor of projective Almost Kahlar manifold. Prove that the manifold M has J-invariant Ricci tensor. Proved that (AK-manifold) M is kahler manifold. Finally, there exists relation between Almost Kahlar manifold (AK-manifold) and Lacally confermal Kähler menifold (LCK-manifeld) has been found.

Screen almost semi-invariant lightlike submanifolds of indefinite Kaehler manifolds

In this paper, we introduce screen almost semi-invariant (SASI)-lightlike submanifolds of indefinite Kaehler manifolds. We obtain the necessary and sufficient condition for the induced connection to be a metric connection on SASI-lightlike submanifolds and construct an example for this manifold. Also, we find some conditions for integrability of distributions and investigate certain characterizations.

Warped Product Quasi Bi-Slant Submanifolds of Kaehler Manifolds

Warped Product Quasi Bi-Slant Submanifolds of Kaehler Manifolds

Infinitesimal Holomorphic Variations of Invariant Submanifolds of Almost Kaehlerian Manifolds

Infinitesimal Holomorphic Variations of Invariant Submanifolds of Almost Kaehlerian Manifolds

Invariant Kähler potentials and symplectic reduction

For a proper Hamiltonian action of a Lie group $G$ on a Kahler manifold $(X,\omega)$ with momentum map $\mu$ we show that the symplectic reduction $\mu^{-1}(0)/G$ is a normal complex space. Every point in $\mu^{-1}(0)$ has a $G$-stable open neighborhood on which $\omega$ and $\mu$ are given by a $G$-invariant Kahler potential. This is used to show that $\mu^{-1}(0)/G$ is a Kahler space. Furthermore we examine the existence of potentials away from $\mu^{-1}(0)$ with both positive and negative results.

Vaisman theorem for lcK spaces

Vaisman's theorem for locally conformally Kahler (lcK) compact manifolds states that any lcK metric on a compact complex manifold which admits a Kahler metric is, in fact, globally conformally Kahler (gcK). In this paper, we extend this theorem to compact complex spaces with singularities.

Semiclassical asymptotics and entropy

We study the entanglement of quantum states associated with submanifolds of Kaehler manifolds. As a motivating example, we discuss the semiclassical asymptotics of entanglement entropy of pure states on the two dimensional sphere with the standard metric.

Semi-slant submanifolds in a locally conformal Kaehler space form

In this paper, we consider semi-slant submanifolds in a locally conformal Kaehler manifold and a locally conformal Kaehler space form. We give inequalities for the length of the second fundamental form and the mean curvature and, using Gauss and Codazzi equations, we get many useful results in locally conformal Kaehler space form.

Generalized Slant lightlike submanifolds of indefinite Kaehler manifolds

This paper introduces the idea of Generalized Slant (GS)-lightlike submanifolds of indefinite Kaehler manifolds, which include semi-slant, screen semi-slant and GCR-lightlike submanifolds as its sub-cases. After defining GS-lightlike submanifolds, we present non-trivial examples followed by a characterization for the existence of this class of lightlike submanifolds. The integrability conditions for various distributions associated with such lightlike submanifolds are then derived. Further, minimal GS-lightlike submanifolds of indefinite Kaehler manifolds are also discussed.

Lightlike Hypersurfaces of an Indefinite Kaehler Manifold with an $(\ell,\,m)$-type Metric Connection

Jin introduced a non-symmetric metric connection, called an {\it $(\ell,m)$-type metric connection} \cite{Jin1, Jin2}. There are two examples of $(\ell, m)$-type: a semi-symmetric metric connection when ${\ell}=1$ and $m=0$ and a quater-symmetric connection for ${\ell}=0$ and $m=1$ . Our purpose is to investigate lightlike hypersurfaces of an indefinite (complex) Kaehler manifolds with an $(\ell,m)$-type metric connection under the tangent characteristic vector field on such hypersurfaces.

Pointwise hemi-slant Riemannian submersions

UDC 517.98 We introduce a new type of submersions, which is called <em>pointwise hemi-slant Riemannian submersions,</em> as a generalization of slant Riemannian submersions, hemi-slant submersions, and pointwise slant submersions from Kaehler manifolds onto Riemannian manifolds. We obtain some geometric interpretations of this kind of submersions with respect to the total manifold, the base manifold, and the fibers. Moreover, we present non-trivial illustrative examples in order to demonstrate the existence of submersions of this kind. Finally, we obtain some curvature equalities and inequalities with respect to a certain basis.

Submersions of CR-warped product submanifolds of a nearly Kaehler manifold

Submersions of CR-warped product submanifolds of a nearly Kaehler manifold

The second fundamental form of the real Kaehler submanifolds

Abstract Let $f\colon M^{2n}\to \mathbb {R}^{2n+p}$ , $2\leq p\leq n-1$ , be an isometric immersion of a Kaehler manifold into Euclidean space. Yan and Zheng (2013, Michigan Mathematical Journal 62, 421–441) conjectured that if the codimension is $p\leq 11$ , then, along any connected component of an open dense subset of $M^{2n}$ , the submanifold is as follows: it is either foliated by holomorphic submanifolds of dimension at least $2n-2p$ with tangent spaces in the kernel of the second fundamental form whose images are open subsets of affine vector subspaces, or it is embedded holomorphically in a Kaehler submanifold of $\mathbb {R}^{2n+p}$ of larger dimension than $2n$ . This bold conjecture was proved by Dajczer and Gromoll just for codimension 3 and then by Yan and Zheng for codimension 4. In this paper, we prove that the second fundamental form of the submanifold behaves pointwise as expected in case that the conjecture is true. This result is a first fundamental step for a possible classification of the nonholomorphic Kaehler submanifolds lying with low codimension in Euclidean space. A counterexample shows that our proof does not work for higher codimension, indicating that proposing $p=11$ in the conjecture as the largest codimension is appropriate.

Pointwise Hemislant Submanifolds in a Complex Space Form

In this paper, pointwise hemislant submanifolds were introduced in a Kahler manifold. The integrability conditions for the distributions which are involved in the definition of a pointwise hemislant submanifold were investigated. In addition, the necessary and sufficient conditions were given for a pointwise hemislant submanifold to be a pointwise hemislant product.