School of Mathematics, Statistics & Computer Science

From left: Professor Fortuné Massamba, Professor Albert Modi and Professor Delia North.

Geometric Structures in Smooth Manifolds Subject of Inaugural Lecture

An academic specialising in differential geometry at UKZN’s School of Mathematics, Statistics and Computer Science, Professor Fortuné Massamba, presented his inaugural lecture on the Pietermaritzburg campus on the subject of geometric structures in smooth manifolds.

Massamba obtained his doctoral degree, which focused on differential geometry, from the Institut de Mathématiques et de Sciences Physiques (IMSP) at the University of Abomey-Calavi in Benin. IMSP is an affiliated centre of the Abdus Salam International Centre for Theoretical Physics in Trieste, Italy.

Massamba’s research interests are in Riemannian and semi-Riemannian geometry, geometric structures on manifolds, CR-submanifolds of almost complex manifolds, contact and symplectic geometry, lightlike geometry, and the geometry of submersions.

His past research focused on moduli spaces of connections in which he enriched the family of metrics on moduli spaces by constructing a class of non-degenerate metrics using the Narasimhan-Ramanan universal connection. His present research topics include Goldberg Conjecture and locally conformal geometry.

Massamba’s inaugural lecture focused on four specific structures – Sasakian, Kenmotsu, cosymplectic and symplectic structures.

‘The contact and almost contact structures are two of the most interesting examples of differential geometric structures,’ explained Massamba. ‘Their theory is a natural generalisation of so-called contact geometry, which has important applications in classical and quantum mechanics.

‘Almost contact metric structures are an odd-dimensional analogue of almost Hermitian structures and there are many important connections between these two classes.’

Massamba proved there are leaves of some distributions of null hypersurfaces in indefinite Sasakian settings which are extrinsic spheres.

He also showed there are foliations on almost Weyl null hypersufaces which are Einstein-Weyl with scalar curvature of constant sign.

‘A solution of the Goldberg conjecture by Sekigawa is that there are no Einstein metric with non-negative Ricci curvature satisfying an invariant on compact symplectic manifolds that admit no Kähler structure,’ said Massamba.

Massamba, who is Congolese, is married with three children.

Words: Sally Frost

Photograph: Albert Hirasen