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Fortuné Massamba

Publications and source records attributed to Fortuné Massamba.

18 recordsLinked to original sources
arXiv2026

Locally conformal almost generalized $f$-cosymplectic manifolds

This paper introduces a new class of geometric structures in almost contact metric geometry, which we call locally conformal almost generalized $f$-cosymplectic manifolds. These are almost contact metric structures $(ϕ, ξ, η, g)$ equipped with a closed Lee form $ω$ and a smooth function $f$ satisfying $$ dη= ω\wedge η, \;\; dΦ= 2fη\wedge Φ+ 2ω\wedge Φ, $$ where $Φ(\cdot, \cdot) = g(\cdot, ϕ\cdot)$ is the second fundamental form. We derive integrability conditions and prove a dimensional dichotomy: in dimension $3$, $ω$ may admit transverse components, while in higher dimensions it must be proportional to $η$. This rigidity, which contrasts with even-dimensional conformal symplectic geometry, is established and illustrated by explicit examples in dimensions $3$ and $5$. The framework generalizes and unifies prior results on locally conformal almost cosymplectic and almost $f$-cosymplectic structures.

math.DG↗
arXiv2025

Timelike conformal fields on closed $3$-manifolds

This paper investigates timelike conformal vector fields on closed Lorentzian $3$-manifolds and shows that, although these fields form a broader class than Killing fields, their behavior in dimension three is nonetheless remarkably rigid. After performing a conformal change of the metric so that the vector field becomes unit and Killing, we analyze the geometry of the flow it generates through the framework of stable Hamiltonian structures and basic cohomology. Our main result proves that any nowhere-vanishing timelike conformal vector field necessarily arises as the Reeb vector field of either a Sasakian structure or a co-Kähler structure. In other words, every such Lorentzian conformal flow is intrinsically "Reeb-like", which forces the underlying geometry to be either contact or cosymplectic. This establishes a striking connection between Lorentzian geometry, Sasakian and co-Kähler structures, and the topology of flows in dimension~$3$.

math.DG↗
arXiv2025

Remark on quasi Sasakian structures

In this work, we revisit quasi-Sasakian geometry in dimension three and examine how these structures interact with the foliation generated by the Reeb vector field and its basic cohomology. Through a deformation-based approach, we show that a closed, orientable $3$-manifold admits a quasi-Sasakian structure precisely when it is either Sasakian or arises as a Kähler mapping torus. In particular, every quasi-Sasakian structure in this setting can be deformed into a Sasakian or a co-Kähler one. This result leads to a complete classification of quasi-Sasakian manifolds in dimension three and highlights the geometric and topological features that distinguish the two cases.

math.DG↗
arXiv2021

Some properties of curvature tensors and foliations of locally conformal almost Kähler manifolds

We investigate a class of locally conformal almost Kähler structures and prove that, under some conditions, this class is a subclass of almost Kähler structures. We show that a locally conformal almost Kähler manifold admits a canonical foliation whose leaves are hypersurfaces with mean curvature vector field proportional to the Lee vector field. The geodesibility of the leaves is also characterized, and their minimality coincides with the incompressibility of the Lee vector field along the leaves.

math.GM↗
arXiv2020

A Ricci-type flow on globally null manifolds and its gradient estimates

Locally, a screen integrable globally null manifold $M$ splits through a Riemannian leaf $M'$ of its screen distribution and a null curve $\mathcal{C}$ tangent to its radical distribution. The leaf $M'$ carries a lot of geometric information about $M$ and, in fact, forms a basis for the study of expanding and non-expanding horizons in black hole theory. In the present paper, we introduce a degenerate Ricci-type flow in $M'$ via the intrinsic Ricci tensor of $M$. Several new gradient estimates regarding the flow are proved.

math.DG↗
arXiv2017

Induced and intrinsic Hashiguchi connections on Finsler submanifolds

We study the geometry of Finsler submanifolds using the pulled-back approach. We define the Finsler normal pulled-back bundle and obtain the induced geometric objects, namely, induced pullback Finsler connection, normal pullback Finsler connection, second fundamental form and shape operator. Under a certain condition, we prove that induced and intrinsic Hashiguchi connections coincide on the pulled-back bundle of Finsler submanifold.

math.GM↗
arXiv2017

Warped products with a Tripathi connection

The warped product $M_1 \times_F M_2$ of two Riemannian manifolds $(M_1,g_1)$ and $(M_2,g_2)$ is the product manifold $M_1 \times M_2$ equipped with the warped product metric $g=g_1 + F^2 g_2$, where $F$ is a positive function on $M_1$. The notion of warped product manifolds is one of the most fruitful generalizations of Riemannian products. Such a notion plays very important roles in differential geometry as well as in physics, especially in general relativity. In this paper we study warped product manifolds endowed with a Tripathi connection. We establish some relationships between the Tripathi connection of the warped product $M$ to those $M_1$ and $M_2$.

math.GM↗
arXiv2017

On twisted Riemannian extensions associated with Szabó metrics

Let $M$ be an $n$-dimensional manifold with a torsion free affine connection $\nabla$ and let $T^*M$ be the cotangent bundle. In this paper, we consider some of the geometrical aspect of a twisted Riemannian extension which provide a link between the affine geometry of $(M,\nabla)$ and the neutral signature pseudo-Riemannian geometry of $T^*M$. We investigate the spectral geometry of the Szabó operator on $M$ and on $T^*M$.

math.DG↗
arXiv2016

Higher order mean curvatures of SAC half-lightlike submanifolds of indefinite almost contact manifolds

We introduce higher order mean curvatures of screen almost conformal (SAC) half-lightlike submanifolds of indefinite contact manifolds, admitting a semi-symmetric non-metric connection, and use them to generalize some known results of [6]. Also, we derive a new set of integration formulae via the divergence of some special vector fields tangent to this submanifold. Several examples are also included to illustrate the main concepts.

math.DG↗
arXiv2016

On total mean curvatures of foliated half-lightlike submanifolds in semi-Riemannian manifolds

We derive total mean curvature integration formulae of a three co-dimensional foliation $\mathcal{F}^{n}$ on a screen integrable half-lightlike submanifold, $M^{n+1}$ in a semi-Riemannian manifold $\overline{M}^{n+3}$. We give generalized differential equations relating to mean curvatures of a totally umbilical half-lightlike submanifold admitting a totally umbilical screen distribution, and show that they are generalizations of those given by [4].

math.DG↗
arXiv2016

Affine Szabó connections on smooth manifolds

In this paper, we introduce a new structure, namely, affine Szabó connection. We prove that, on $2$-dimensional affine manifolds, the affine Szabó structure is equivalent to one of the cyclic parallelism of the Ricci tensor. A characterization for locally homogeneous affine Szabó surface is obtained. Examples of two- and three-dimensional affine Szabó manifolds are also given.

math.DG↗
arXiv2016

Some remarks on quasi generalized CR-null geometry in indefinite nearly cosymplectic manifolds

In [21], the authors initiated the study of quasi generalized CR (QGCR)-null submanifolds. In this paper, attention is drawn to some distributions on ascreen QGCR-null submanifolds in an indefinite nearly cosymplectic manifold. We characterize totally umbilical and irrotational ascreen QGCR-null submanifolds. We finally discuss the geometric effects of geodesity conditions on such submanifold.

math.DG↗
arXiv2016

A note on quasi generalized CR-lightlike geometry in indefinite nearly $μ$-Sasakian manifold

The concept of quasi generalized CR-lightlike was first introduced by the authors in [18]. In this paper, we focus on ascreen and co-screen quasi generalized CR-lightlike submanifolds of indefinite nearly $μ$-Sasakian manifold. We prove an existence theorem for minimal ascreen quasi generalized CR-lightlike submanifolds admitting a metric connection. Classification theorems on nearly parallel and auto-parallel distributions on a co-screen quasi generalized CR-lightlike submanifold are also given. Several examples are also constructed, where necessary, to illustrate the main ideas.

math.DG↗
arXiv2016

Sasakian Finsler structures on pulled-back bundle

Under a pulled-back approach given in [1] and firstly presented in [2], we introduce, in this paper, the concepts of almost contact and normal almost contact Finsler structures on the pulled-back bundle. Properties of structures partly Sasakians are studied. Using the hh-curvature tensor of Chern connection given in [2], we obtain some characterizations of horizontally Finslerian K-contact structures via the horizontal Ricci tensor and the flag curvature.

math.DG↗
arXiv2016

Quasi Generalized CR-lightlike submanifolds of indefinite nearly Sasakian manifolds

In this paper, we introduce and study a new class of CR-lightlike submanifold of an indefinite nearly Sasakian manifold, called Quasi Generalized Cauchy-Riemann (QGCR) lightlike submanifold. We give some characterization theorems for the existence of QGCR-lightlike submanifolds and finally derive necessary and sufficient conditions for some distributions to be integrable.

math.DG↗
arXiv2016

On three dimensional affine Szabó manifolds

In this paper, we consider the cyclic parallel Ricci tensor condition, which is a necessary condition for an affine manifold to be Szabó. We show that, in dimension $3$, there are affine manifolds which satisfy the cyclic parallel Ricci tensor but are not Szabó. Conversely, it is known that in dimension $2$, the cyclic parallel Ricci tensor forces the affine manifold to be Szabó. Examples of $3$-dimensional affine Szabo manifolds are also given. Finally, we give some properties of Riemannian extensions defined on the cotangent bundle over an affine Szabó manifold.

math.DG↗