Professeur.Aboubacar NIBIRANTIZA

Nom et prénom         :Aboubacar NIBIRANTIZA

Faculté/Institut         : Institut de Pédagogie Appliquée (IPA)

Centre de recherche    : Centre Universitaire de Recherche et de Pedagogie Appliquees aux Sciences(CURPAS) /Laboratoire des Sciences Exactes et Appliquees (LSEA)

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• The research paper investigates the computation of Casimir operators on sl 2-modules associated with linear differential operators and symbols on the real line. The study considers spaces of differential operators and principal symbols related to tensor densities, and derives explicit formulas for the Casimir operators. It extends previously known results about sl 2 -modules and Schur’s Lemma, enriching the understanding of their role in differential geometry and representation theory.
  publier le 2025-11-25 07:20:39

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• In this paper, we give a new presentation of the classification of simple real Jordan algebras. They are classified in four types: type I, type II, type III and type IV and to obtain those types we have to classify the involution classes of Euclidean simple Jordan algebras. We specify which involution is adapted and this one defines the type of simple real Jordan algebra classified.
  publier le 2025-11-25 07:38:47

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• In this paper, we give a new presentation of the classification of simple real Jordan algebras. They are classified in four types: type I, type II, type III and type IV and to obtain those types we have to classify the involution classes of Euclidean simple Jordan algebras. We specify which involution is adapted and this one defines the type of simple real Jordan algebra classified.
  publier le 2025-11-25 07:40:32

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• In this paper,we compute the invariant geometry of the statistical manifold of the normal distributions by using the divergence approach. In order to give the isometries, we investigate the component functions of a Killing vector field for the Fisher information metric on the statistical manifold of Gaussian distributions of probabilities. They are harmonic conjugate and then, they are both harmonic functions. Finally, we describe the form of its Killing vector fields.
  publier le 2025-11-25 07:56:35

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• We establish the links between the lightlike geometry and basics invariants of the associated semi-Riemannian geometry on r-lightlike submanifold and semi-Riemannian constructed from a semi-Riemannian ambient. Then we establish some basic inequalities, involving the scalar curvature and shape operator on r-lightlike coisotropic submanifold in semi-Riemannian manifold. Equality cases are also discussed.
  publier le 2025-11-25 08:07:07

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