Kahler Manifold Research Articles

Nearly Kaehler manifolds admitting a closed conformal vector field

Nearly Kaehler manifolds admitting a closed conformal vector field

Sequential warped product submanifolds in nearly Kaehler manifolds

A new class of warped product manifolds which is known as sequential warped product manifolds have been defined in [15] and studied in detail in [9]. This article is dedicated to study sequential warped product submanifolds having factors holomorphic, totally real and pointwise slant submanifolds of nearly Kaehler manifolds. We obtained Chen?s inequality for sequential warped product submanifolds involving second fundamental form and warping functions.

Sasakian surfaces of invariable holomorphic sectional curvature in Hyper-Kaehlerian manifolds

Negi and Bisht (2019) measured almost contact hypersurfaces of a Kaehlerian manifold. They (Negi and Bisht 2022) also calculated hypersurface Properties of Almost Contact Kaehlerian Manifolds. In this paper, the author has defined and studied the Sasakian surfaces of invariable holomorphic sectional curvature in Hyper-Kaehlerian manifolds and established several theorems.

Curvature Tensors in a Kaehler Manifold with Semi-Symmetric Metric Connection

Curvature Tensors in a Kaehler Manifold with Semi-Symmetric Metric Connection

Decomposition of Riemannian Recurrent Curvature Tensor Manifolds of First Order

Takano [6] premeditated decomposition of curvature tensor in a recurrent Riemannian space. After that, Negi and Bisht [3] defined and deliberated decomposition of recurrent curvature tensor fields in a Kaehlerian manifolds of first order. We have calculated the decomposition of Riemannian recurrent curvature tensor manifolds of first order and some theorems established using the decomposition tensor field.

Positivity and the Kodaira embedding theorem

Kodaira embedding theorem provides an effective characterization of projectivity of a Kahler manifold in terms the second cohomology. Recently X. Yang [21] proved that any compact Kahler manifold with positive holomorphic sectional curvature must be projective. This gives a metric criterion of the projectivity in terms of its curvature. In this note, we prove that any compact Kahler manifold with positive 2nd scalar curvature (which is the average of holomorphic sectional curvature over 2-dimensional subspaces of the tangent space) must be projective. In view of generic 2-tori being non-abelian, this new curvature characterization is sharp in certain sense.

A STUDY ON MANIFOLD KAEHLERIAIN SPACE

This work delves into the space-time theory of the 4-dimensional Kaehler manifold. Since the isotropic pressure, energy density, and energy momentum tensor all vanish in a perfect fluid Kaehler space-time manifold, we have established that this space-time manifold is an Einstein manifold and studied the Einstein equation with a cosmological constant in it. Finally, we demonstrated that, on a conformally flat, perfectly fluid Kaehler space-time manifold, the velocity vector field is infinitesimally spatially isotropic. Ideal fluid dilution to the point where only Ricci and minimal symmetry hold. We have proven that Kaehler space-time manifolds have either 0 scalar curvature or a connection between the respective rho and alpha vector fields via g(rho,alpha) = 4. To conclude, we have proved that a Kaehler space-time manifold cannot have both perfect fluidity and non-zero scalar curvature (weak Ricci symmetry).

Formulating E- & T-Model Inflation in Supergravity

We present novel realizations of E- and T-model inflation within Supergravity which are largely associated with the existence of a pole of order one and two respectively in the kinetic term of the inflaton superfield. This pole arises due to the selected logarithmic Kahler potentials K, which parameterize hyperbolic manifolds with scalar curvature related to the coefficient (−N) < 0 of a logarithmic term. The associated superpotential W exhibits the same R charge with the inflaton-accompanying superfield and includes all the allowed terms. The role of the inflaton can be played by a gauge singlet or non-singlet superfield. Models with one logarithmic term in K for the inflaton, require N = 2, some tuning – of the order of 10−5 – between the terms of W and predict a tensor-to-scalar ratio r at the level of 0.001. The tuning can be totally eluded for more structured K’s, with N values increasing with r and spectral index close or even equal to its present central observational value.

НЕКОТОРЫЕ ВОПРОСЫ ГЕОМЕТРИИ ЛОКАЛЬНО КОНФОРМНО-КЕЛЕРОВЫХ МНОГООБРАЗИЙ

Torso-forming vector fields, as well as their special cases (concircular, special concircular and recurrent) are used in many areas of differential geometry, for example, in conformal, geodesic, almost geodesic, holomorphically projective and other mappings and transformations. The presence of torso-forming vector fields on the space under consideration makes the geometry of this space more meaningful. It is of interest to study the geometry of spaces that admit recurrent vector fields. In this paper, the authors consider locally conformally Kahler manifolds with a recurrent Lie vector. Such manifolds are called recurrent locally conformally Kahler manifolds. The Lie form and the Lie vector are calculated explicitly. It is proved that the Lie vector of a locally conformally Kahler manifold of constant curvature is a concircular field. A recurrence criterion for a conformally flat locally conformally Kahler manifold is obtained. Some properties of conformally flat locally conformally Kahler manifolds are proved. It is proved that a compact manifold of constant curvature does not admit its own recurrent locally conformal Kahler structure.

Loops, local corrections and warping in the LVS and other type IIB models

To establish metastable de Sitter vacua or even just scale-separated AdS, control over perturbative corrections to the string-derived leading-order 4d lagrangian is crucial. Such corrections can be classified in three types: first, there are genuine loop effects, insensitive to the UV completion of the 10d theory. Second, there are local α′ corrections or, equivalently, 10d higher-dimension operators which may or may not be related to loop-effects. Third, warping corrections affect the 4d Kahler potential but are expected not to violate the 4d no-scale structure. With this classification in mind, we attempt to derive the Berg-Haack-Pajer conjecture for Kahler corrections in type-IIB Calabi-Yau orientifolds and extend it to include further terms. This is crucial since the interesting applications of this conjecture are in the context of generic Calabi-Yau geometries rather than in the torus-based models from which the main motivation originally stems. As an important by-product, we resolve a known apparent inconsistency between the parametric behaviour of string loop results and field-theoretic expectations. Our findings lead to some interesting new statements concerning loop effects associated with blowup-cycles, loop corrections in fibre inflation, and possible logarithmic effects in the Kahler and scalar potential.

Generic lightlike submanifolds of an indefinite Kaehler manifold with an $(\ell, m)$-type metric connection

We study generic lightlike submanifolds $M$ of an indefinite Kaehler manifold $\bar{M}$ or an indefinite complex space form $\bar{M}(c)$ with an $(\ell, m)$-type metric connection subject such that the characteristic vector field $\zeta$ of $\bar{M}$ belongs to our screen distribution $S(TM)$ of $M$.

Analytic Vector Fields on an Almost Hermite Manifolds

This communication respectively deals with contravariant almost analytic vector fields and contravariant almost analytic vector fields on a Kaehler manifold admitting semi- symmetric metric connection. The nature and behavior of curvature tensor K ̃(x,y,z) associated with semi-symmetric metric connection and also that of concircular curvature tensor C(X,Y,Z) has also been studied.

Restricted volumes on Kähler manifolds

We study numerical restricted volumes of (1,1) classes on compact Kahler manifolds, as introduced by Boucksom. Inspired by work of Ein-Lazarsfeld-Mustata-Nakamaye-Popa on restricted volumes of line bundles on projective manifolds, we pose a natural conjecture to the effect that irreducible components of the non-Kahler locus of a big class should have vanishing numerical restricted volume. We prove this conjecture when the class has a Zariski decomposition, and give several applications.

Characterizations of pseudo-umbilical submanifolds of Kaehler manifolds by means of specific types

Characterizations of pseudo-umbilical submanifolds of Kaehler manifolds by means of specific types

Pointwise slant Riemannian maps from Kaehler manifolds

Pointwise slant submanifolds were introduced by Chen and Garay (2012) [16] as a natural generalization of slant submanifolds. On the other hand, pointwise slant submersions were defined by Lee and Şahin (2014) [29] as a natural generalization of slant submersions. In this paper, as a generalization of pointwise slant submanifolds and pointwise slant submersions, we introduce pointwise slant Riemannian maps from almost Hermitian manifolds to Riemannian manifolds, present examples and characterizations. We investigate the geometry of foliations which are arisen from the definition of a pointwise slant Riemannian map and obtain decomposition theorems by using the existence of pointwise slant Riemannian maps. We also investigate the harmonicity of such maps and find necessary and sufficient conditions for pointwise slant Riemannian maps to be totally geodesic. Finally, we study some curvature relations in complex space forms, involving Casorati curvatures for pointwise slant Riemannian maps.

Pluriharmonic conformal bi-slant Riemannian maps

In this study, notion of pluriharmonic map applied onto conformal bi-slant Riemannian maps from a Kaehler manifold to a Riemannian manifold to examine its geometric properties. Such that, relations between pluriharmonic map, horizontally homothetic map and totally geodesic map were obtained.

Conformal Kaehler Euclidean submanifolds

Let f:M2n→R2n+ℓ, n≥5, be a conformal immersion into Euclidean space with codimension ℓ where M2n is a Kaehler manifold of complex dimension n free of points where all sectional curvatures vanish. For codimension ℓ=1 or ℓ=2 we show that at least locally such a submanifold can always be obtained in a rather simple way, namely, from an isometric immersion of the Kaehler manifold M2n into either R2n+1 or R2n+2, the latter being a class of submanifolds already extensively studied.

Almost paracomplex structures on 4-manifolds

Reflection in a line in Euclidean 3-space defines an almost paracomplex structure on the space of all oriented lines, isometric with respect to the canonical neutral Kaehler metric. Beyond Euclidean 3-space, the space of oriented geodesics of any real 3-dimensional space form admits both isometric and anti-isometric paracomplex structures.This paper considers the existence or otherwise of isometric and anti-isometric almost paracomplex structures j on a pseudo-Riemannian 4-manifold (M,g), such that j is parallel with respect to the Levi-Civita connection of g. It is shown that if an isometric or anti-isometric almost paracomplex structure on a conformally flat manifold is parallel, then the scalar curvature of the metric must be zero. In addition, it is found that j is parallel iff the eigenplanes are tangent to a pair of mutually orthogonal foliations by totally geodesic surfaces.The composition of a Riemannian metric with an isometric almost paracomplex structure j yields a neutral metric g′. It is proven that if j is parallel, then g is Einstein iff g′ is conformally flat and scalar flat.The vanishing of the Hirzebruch signature is found to be a necessary topological condition for a closed 4-manifold to admit an Einstein metric with a parallel isometric paracomplex structure. Thus, while the K3 manifold admits an Einstein metric with an isometric paracomplex structure, it cannot be parallel. The same holds true for certain connected sums of complex projective 2-space and its conjugate.

Quasi Bi-Slant Submanifolds of Kaehler Manifolds

In this paper, we introduce the new notion of quasi bi-slant submanifolds of almost Hermitian manifolds. Necessary and sufficient conditions for the integrability of distributions which are involved in the definition of such submanifolds of a Kaehler manifold are obtained. We also investigate the necessary and sufficient conditions for these submanifolds of Kaehler manifolds to be totally geodesic and study the geometry of foliations determined by the above distributions. Finally, we obtain the necessary and sufficient conditions for a quasi bi-slant submanifold to be local product Riemannian manifold and also construct some examples of such submanifolds.

Horizontally Conformal Submersions from CR-Submanifolds of Locally Conformal Quaternionic Kaehler Manifolds

Horizontally Conformal Submersions from CR-Submanifolds of Locally Conformal Quaternionic Kaehler Manifolds