9 papers
Killing Vectors and Bochner-Type Theorems in Pseudo-Riemannian Hom-Lie Algebras
Raymond Hounnonkpe, Ibrahima Bakayoko, Emmanuel Gnandi +1
In this paper, we study pseudo-Riemannian Hom-Lie algebras. We establish Hom-versions of the classical Bochner theorem in both the Riemannian and Lorentzian settings. Finally, we p…
Ricci Curvature and Betti Numbers of Hessian Manifolds
Emmanuel Gnandi, Stéphane Puechmorel
We study Ricci curvature properties of Hessian metrics on the leaves of the codimension-one foliation generated by the first Koszul form of a closed or…
Timelike conformal fields on closed -manifolds
Emmanuel Gnandi, Fortuné Massamba
This paper investigates timelike conformal vector fields on closed Lorentzian -manifolds and shows that, although these fields form a broader class than Killing fields, their be…
Remark on quasi Sasakian structures
Emmanuel Gnandi, Fortuné Massamba
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 co…
On the parity of the Betti numbers of 3-manifolds with a parallel vector field
Emmanuel Gnandi, Raymond A. Hounnonkpe
The question of whether a closed, orientable manifold can admit a nontrivial vector field that is parallel with respect to some Riemannian metric is a classical problem in Differen…
Construction of Exponential Families from Statistical Manifolds
Emmanuel Gnandi
We investigate the construction of exponential families from statistical manifolds, a central problem in information geometry. We prove that every compact statistical manifold admi…
The topology of 3-dimensional Hessian manifolds
Emmanuel Gnandi
We investigate the global topology of 3-dimensional Hessian manifolds. We prove that any compact, orientable 3-dimensional Hessian manifold is either a Hantzsche-Wendt manifold or…
Any Kähler metric is a Fisher information metric
Emmanuel Gnandi
The Fisher information metric or the Fisher-Rao metric corresponds to a natural Riemannian metric defined on a parameterized family of probability density functions. As in the case…
From Dual Connections to Almost Contact Structures
E. Gnandi, S. Puechmorel
A dualistic structure on a smooth Riemaniann manifold is a triple with a Riemaniann metric and an affine connection, generally assumed to be torsion…