Fortuné Massamba
Titre / Grade : Professeur
Prénom : Fortuné
Nom : MASSAMBA
Institution : School of Mathematics, Statistics and Computer Science University of KwaZulu-Natal
Pays : Afrique du Sud
Email : massamba@ukzn.ac.za
Titre du cours : Some developments in almost contact and symplectic geometry
Résumé du cours :
The contact and almost contact structures are two of the most interesting examples
of differential geometric structures. Their theory is a natural generalization 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 exist many important connections between these two classes.
In this course, we pay attention to some specific structures among the 4096 existing classes
of almost contact metric structures and 16 classes of almost Hermitian ones, namely, Sasakian,
cosymplectic and symplectic structures.
A solution of the Goldberg conjecture by Sekigawa is that there exists no Einstein metric
with non-negative Ricci curvature satisfying an invariant on compact symplectic manifolds
that admit no Kähler structure.
