2 research outputs found
k-symplectic affine Kie algebras
The notion of k-symplectic structures was introduced by A. Awane in his dissertation in 1984. Here we are interested by the classification of Lie algebras provided with such a structure. We introduce also the notion of affine structure associated to a K-symplectic structure on a Lie algebr
On Some Geometric Structures Associated to a k-Symplectic Manifold
A canonical connection is attached to any k-symplectic manifold. We study the
properties of this connection and its geometric applications to k-symplectic
manifolds. In particular we prove that, under some natural assumption, any
ksymplectic manifold admits an Ehresmann connection, discussing some
corollaries of this result, and we find vanishing theorems for characteristic
classes on a k-symplectic manifold.Comment: To appear on J. Phys. A: Math. Theo