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université du Bururndi
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Professeur. Aboubacar NIBIRANTIZA

University : University of Burundi
Faculty : Institute of Applied Pedagogy (IPA)
Research Center : Centre Universitaire de Recherche et de Pedagogie Appliquees aux Sciences(CURPAS) /Laboratoire des Sciences Exactes et Appliquees (LSEA)


Doctor of Science with a specialization in Mathematics, academic degree obtained on July 23, 2014 at the University of Liège (Belgium).
Professor/Researcher in the Department of Mathematics at the Institute of Applied Pedagogy, University of Burundi (Bujumbura).
Appointed Professor in April 2020 by a ministerial decree of Burundi.
Recipient of the Simons–IMU Africa Fellowship in 2021.
Researcher in the fields of equivariant and geometric quantization, information geometry (statistical manifolds), representation theory of Lie groups/Lie algebras, and homogeneous spaces.
Recognized internationally through his IMU–Simons fellowship and collaborates with institutions in Europe (such as the Institut Fourier in France).
A key contributor to training and teaching activities, particularly in bachelor’s and master’s programs in Science in Burundi.
📘 Syllabus du cours d'Algèbre commutative
📅 Published on 2025-11-22 16:06:15
📘 Syllabus de Theorie des groupes
📅 Published on 2026-01-30 10:50:18
📘 Syllabus de Geometrie II
📅 Published on 2026-01-30 11:04:21
📘 Programmation par la pratique
📅 Published on 2026-05-11 10:51:25
📘 Syllabus du cours de Théorie des fibrés
📅 Published on 2026-05-17 07:56:53
📄 In this paper, we express the geometry of (M,F) in term of f and the geometry of (bar M, bar F). Curvatures are calculated in the Berwald case. An example of a twisted product Berwald metric is given for n=3.
📅 Published on 2026-05-17 08:17:25
📄 Let F be a Finslerian metric on a C? manifold M . We de?ne horizontal and vertical Laplace type operators for C? functions on the slit tangent bundle T? M of the Finslerian manifold (M, F ). The expression of the vertical Laplacian ? v , in local coordinates, is obtained by using the Chern connection on the pulled-back tangent bundle. Furthermore, we prove the vertical divergence lemma and we show that if (M, F ) is an oriented Finslerian manifold then every globally de?ned function u on T? M , with ? v u ? 0 everywhere or ? v u ? 0 everywhere, must be independant of directional arguments.
📅 Published on 2026-05-17 08:09:25
📄 Coadjoint orbits provide a fundamental link between symplectic geometry and the representation theory of Lie groups, as formalized by the orbit method of Kirillov. In this paper, we investigate the spectral properties of the Casimir operator in relation to the geometry of coadjoint orbits and their quantization. We establish a spectral rigidity phenomenon: for compact semisimple Lie groups, the eigenvalue of the Casimir operator determines the corresponding coadjoint orbit and the associated irreducible representation. This rigidity is shown to be independent of the choice of G-invariant metric on the orbit, highlighting the intrinsic algebraic nature of the Casimir operator. We provide explicit computations in the case of SU (2), where coadjoint orbits are 2-spheres, and analyze the relationship between the Casimir operator and the Laplace–Beltrami operator under metric variations. We further extend the discussion to real semisimple Lie groups, where rigidity persists in a weaker form through the infinitesimal character and the Harish-Chandra isomorphism. Our results clarify the role of the Casimir operator as a bridge between geometry, spectral theory, and geometric quantization.
📅 Published on 2026-05-17 08:06:14
📄 Let F be a Finslerian metric on a C^? manifold M . We de?ne horizontal and vertical Laplace type operators for C^? functions on the slit tangent bundle T? M of the Finslerian manifold (M, F ). The expression of the vertical Laplacian ?^v , in local coordinates, is obtained by using the Chern connection on the pulled-back tangent bundle. Furthermore, we prove the vertical divergence lemma and we show that if (M, F ) is an oriented Finslerian manifold then every globally de?ned function u on T? M , with ?^v u ? 0 everywhere or ?^v u ? 0 everywhere, must be independant of directional arguments.
📅 Published on 2026-05-11 16:25:45
📄 We present a geometric interpretation of the viscous Burgers equation in terms of an abelian logarithmic connection on a complex line bundle. The ve- locity field is shown to define the local component of a gauge potential, while the Cole-Hopf transformation corresponds to a logarithmic trivialization of the associated flat connection. In this framework, the nonlinear Burgers dy- namics is reinterpreted as an evolution on the space of connections, whereas the Cole-Hopf transform induces a linear Schrödinger-type (heat) equation on sections of the bundle. We analyze the resulting gauge structure and show that the construction can be organized using concepts from prequantum ge- ometry, without implying a genuine quantization scheme. The flatness of the connection and the absence of a non-degenerate symplectic form are dis- cussed as intrinsic obstructions to full quantization. This viewpoint clarifies both the linearization mechanism of the Cole-Hopf transformation and its ge- ometric limitations. In this paper, no new analytical results are claimed.
📅 Published on 2026-05-11 09:16:51
📄 In this paper, we consider Osserman conditions on lightlike warped product (sub-)manifolds with respect to the Jacobi Operator. We define the Jacobi operator for lightlike warped product manifold and introduce a study of lightlike warped product Osserman manifolds. For the coisotropic case with totally degenerates first factor, we prove that this class consists of Einstein and locally Osserman lightlike warped product.
📅 Published on 2026-01-30 10:42:47
📄 Lightlike warped product manifolds are considered in this paper. The geometry of lightlike submanifolds is difficult to study since the normal vector bundle intersects with the tangent bundle. Due to the degenerate metric, the induced connection is not metric and it follows that the Riemannian curvature tensor is not algebraic. In this situation, some basic techniques of calulus are not useable. In this paper, we consider lightlike warped product as submanifold of semi-Riemannian manifold and establish some remarkable geometric properties from which we establish some conditions on the algebraicity of the induced Riemannian curvature tensor.
📅 Published on 2026-01-30 10:32:50
📄 We consider the space of differential operators D?? acting between ?- and ?-densities defined on S1|2 endowed with its standard contact structure. This contact structure allows one to define a filtration on D?? which is finer than the classical one, obtained by writting a differential operator in terms of the partial derivatives with respect to the different coordinates. The space D?? and the associated graded space of symbols S? (?=???) can be considered as spo(2|2)-modules, where spo(2|2) is the Lie superalgebra of contact projective vector fields on S1|2. We show in this paper that there is a unique isomorphism of spo(2|2)-modules between S? and D?? that preserves the principal symbol (i.e. an spo(2|2)-equivariant quantization) for some values of ? called non-critical values. Moreover, we give an explicit formula for this isomorphism, extending in this way the results of [Mellouli N., SIGMA 5 (2009), 111, 11 pages] which were established for second-order differential operators. The method used here to build the spo(2|2)-equivariant quantization is the same as the one used in [Mathonet P., Radoux F., Lett. Math. Phys. 98 (2011), 311-331] to prove the existence of a pgl(p+1|q)-equivariant quantization on Rp|q.
📅 Published on 2026-01-30 10:18:35
📄 In this paper, we show that the Lie superalgebra spo ( 2 l + 2| n ) is into the intersection of Lie superalgebra of contact vector fields K ( 2 l + 1| n ) and the Lie superalgebra of projective vector fields pgl ( 2 l + 2 |n ). Explicitly, we use the embedding of a Lie superalgebra constituted of matrices belonging to gl ( 2 l + 2| n ) into Vect ( R 2 l + 1 |n ) . We generalize thus in superdimension 2 l + 1 ? n , the matrix realization described in [7] on S^1/2 . We mention that the intersection spo ( 2 l + 2 |n ) = pgl ( 2 l + 2 n ) ? K ( 2 l + 1 n ) that we prove here, in super case, has been proved on R^2 l + 2 in even case in [4].
📅 Published on 2026-01-30 10:12:03
📄 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.
📅 Published on 2025-11-25 08:07:07
📞 Phone : +25768279503
✉️ Email : aboubacar.nibirantiza@ub.edu.bi