arXiv research

The aim of this paper is to present the first examples of compact, simply connected holomorphically pseudosymmetric Kahler manifolds.

The aim of this paper is to present examples of Kahler holomorphically pseudosymmetric metrics on the projective space CP^n.

For compact Kählerian manifolds, the holomorphic pseudosymmetry reduces to the local symmetry if additionally the scalar curvature is constant and the structure function is non-negative. Similarly, the holomorphic Ricci-pseudosymmetry reduces to the Ricci-symmetry under these additional assumptions. We construct exampl…

The study characterizes symmetries in Kaehler manifolds.

The paper explores symmetries in Kähler manifolds using Ricci tensor properties.

The object of the present paper is to study some types of Ricci pseudosymmetric $(LCS)_n$-manifolds whose metric is Ricci soliton. We found the conditions when Ricci soliton on concircular Ricci pseudosymmetric, projective Ricci pseudosymmetric, $W_{3}$-Ricci pseudosymmetric, conharmonic Ricci pseudosymmetric, conforma…

The paper finds conditions for pseudosymmetric spacetimes to be perfect fluids.

Definition of $({\cal T}_{a},{\cal T}_{b})$-pseudosymmetric semi-Riemannian manifold is given. $({\cal T}_{a},{\cal T}_{b})$-pseudosy mmetric $(N(k),ξ)$-semi-Riemannian manifolds are classified. Some results for ${\cal T}_{a}$-pseudosymmetric $(N(k),ξ)$-semi-Riemannian manifolds are obtained. $({\cal T}_{a},{\cal T}_{b…

In the literature, there are two different notions of pseudosymmetric manifolds, one by Chaki [7] and other by Deszcz [16], and there are many papers related to these notions. The object of the present paper is to deduce necessary and sufficient conditions for a Chaki pseudosymmetric [7] (resp. pseudo Ricci symmetric […

The curvature properties of Robinson-Trautman metric have been investigated. It is shown that Robinson-Trautman metric admits several kinds of pseudosymmetric type structures such as Weyl pseudosymmetric, Ricci pseudosymmetric, pseudosymmetric Weyl conformal curvature tensor etc. Also it is shown that the difference $R…

The object of the present paper is to study the characterization of warped product manifolds satisfying some pseudosymmetric type conditions, especially, due to projective curvature tensor. For this purpose we consider a warped product manifold satisfying the pseudosymmetric type condition $R\cdot R = L_1 Q(g,R) + L_2 …

This paper aims to investigate the curvature restricted geometric properties admitted by Melvin magnetic spacetime metric, a warped product metric with $1$-dimensional fibre. For this, we have considered a Melvin type static, cylindrically symmetric spacetime metric in Weyl form and it is found that such metric, in gen…

In this paper we classify Ricci-generalized pseudosymmetric $(κ, μ)$-contact metric manifolds in the sense of Deszcz .

The paper investigates various generalizations of semisymmetric and pseudosymmetric manifolds.

Investigates geometric properties of Bardeen black hole spacetime.

The charged Nariai spacetimes are the exact solutions of Einstein-Maxwell field equations with positive cosmological constant and such a spacetime is the direct topological product of a $2$-dimentional de-Sitter spacetime with a round $2$-sphere of constant radius. The present paper deals with the investigation of curv…

The projective curvature tensor $P$ is invariant under a geodesic preserving transformation on a semi-Riemannian manifold. It is well known that $P$ is not a generalized curvature tensor and hence it possesses different geometric properties than other generalized curvature tensors. The main object of the present paper …

Study properties of hyperbolic Yamabe solitons in submanifolds.

We determine a particular class of Roter type warped product manifolds. We show that every manifold of that class admits a geodesic mapping onto a some Roter type warped product manifold. Moreover, both geodesically related manifolds are pseudosymmetric of constant type.

The object of this paper is study $(ε)$-para-Sasakian 3-manifolds satisfying certain conditions on the $\mathcal{Z}$ tensor. We characterize, $\mathcal{Z}$-symmetric; $\mathcal{Z}$-semisymmetric; $\mathcal{Z}$-pseudosymmetric; and projectively $\mathcal{Z}$-semisymmetric conditions on an $(ε)$-para-Sasakian 3-manifold.

The main objective of the present paper is to investigate the curvature properties of generalized pp-wave metric. It is shown that generalized pp-wave spacetime is Ricci generalized pseudosymmetric, 2-quasi-Einstein and generalized quasi-Einstein in the sense of Chaki. As a special case it is shown that pp-wave spaceti…

The paper examines geometric properties of a specific black hole spacetime.

In this paper, $N(κ)$-contact metric manifolds satisfying the conditions $\widetilde{C}(ξ,X)\cdot\widetilde{C}=0$, $\widetilde{C}(ξ,X)\cdot R=0$, $\widetilde{C}(ξ,X)\cdot S=0$, $\widetilde{C}(ξ,X)\cdot C=0$, $C\cdot S=0$ and $R\cdot C=f_{C}Q(g,C)$ have been investigated and obtained their classification. Among others i…

In this paper we study the 3-dimensional $(\varepsilon)$-para Sasakian manifolds. We obtain an necessary and sufficient condition for an $(\varepsilon )$-para Sasakian 3 -manifold to be an indefinite space form. We show that a Ricci-semi-symmetric $(\varepsilon)$-para Sasakian 3 -manifold is an indefinite space form…

As a generalization of the Schwarzschild solution, Vaidya presented a radiating metric to develop a model of the exterior of a star including its radiation field, called Vaidya metric. The present paper deals with the investigation on the curvature properties of Vaidya metric. It is shown that Vaidya metric can be cons…

In this paper, we develop holomorphic Jacobi structures. Holomorphic Jacobi manifolds are in one-to-one correspondence with certain homogeneous holomorphic Poisson manifolds. Furthermore, holomorphic Poisson manifolds can be looked at as special cases of holomorphic Jacobi manifolds. We show that holomorphic Jacobi str…

Develops theory of d-holomorphic connections on Klein surfaces.

Survey on holomorphic structures on complex manifolds.

The goal of this paper is to study the theory of last multipliers in the framework of complex manifolds with a fixed holomorphic volume form. The motivation of our study is based on the equivalence between a holomorphic ODE system and an associated real ODE system and we are interested how we can relate holomorphic las…

Holomorphic Lie algebroid connections on Riemann surfaces are characterized.

Classifies Kähler metrics with constant holomorphic curvature.

We introduce holomorphic Riemannian maps between almost Hermitian manifolds as a generalization of holomorphic submanifolds and holomorphic submersions, give examples and obtain a geometric characterization of harmonic holomorphic Riemannian maps from almost Hermitian manifolds to Kaehler manifolds.

New proof shows holomorphic sectional curvature fully determines curvature tensor.

Formula derived for holomorphic Poisson blow-ups.

Study on holomorphic isometries between complex domains, revealing geometric properties.

Study finds conditions for minimum of Donaldson's functional on Higgs bundles with non-holomorphic Higgs fields.

This is the second part of a series of two papers dedicated to a systematic study of holomorphic Jacobi structures. In the first part, we introduced and study the concept of a holomorphic Jacobi manifold in a very natural way as well as various tools. In the present paper, we solve the integration problem for holomorph…

Introduces quasi-holomorphic maps and their properties.

Holomorphic cylinders converge to disks joined by flow lines.

We study holomorphic Poisson manifolds and holomorphic Lie algebroids from the viewpoint of real Poisson geometry. We give a characterization of holomorphic Poisson structures in terms of the Poisson Nijenhuis structures of Magri-Morosi and describe a double complex which computes the holomorphic Poisson cohomology. A …

Holomorphic structures on Oeljeklaus-Toma manifolds are shown to be locally homogeneous.

Paper describes holomorphic polyvector fields on toric varieties.

Let $E$ be a closed set in the Riemann sphere $\widehat{\mathbb{C}}$. We consider a holomorphic motion $φ$ of $E$ over a complex manifold $M$, that is, a holomorphic family of injections on $E$ parametrized by $M$. It is known that if $M$ is the unit disk $Δ$ in the complex plane, then any holomorphic motion of $E$ ove…

Study connections on complex Riemann surfaces for Lie algebroid structures.

The study classifies holomorphic projective connections on complex threefolds.

Study on complex tori foliations and flat geometries.

Introduces new holomorphic contact structures and proves unobstructedness theorems.

Every holomorphic effective parabolic or reductive geometry on a domain over a Stein manifold extends uniquely to the envelope of holomorphy of the domain. This result completes the open problems of my earlier paper on extension of holomorphic geometric structures on complex manifolds. We use this result to classify th…