Let (M, I, J,K) be a compact hypercomplex manifold admitting a special kind of quaternionic-Hermitian metric called an HKT-metric. Assume that the canonical bundle of (M, I) is trivial as a holomorphic line bundle. We show that the holonomy of canonical torsion-free connection called Obata connection onM is contained in SL(n,H). In Appendix we apply these arguments to compact nilmanifolds which...

This paper studies the canonical symmetric connection $\nabla$ associated to any Lie group $G$. The salient properties of are stated and proved. symmetries geodesic system a general linear formulated. results then applied in special case where algebra $\g$ $G$, has codimension one abelian nilradical. conditions that determine symmetry such completely integrated. Finally obtained compared with s...

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 assumptions, any ksymplectic manifold admits an Ehresmann connection, discuss some corollaries of this result and find vanishing theorems for characteristic classes on a k-symplectic...

In this paper the problem of compatibility between a nonlinear connection and other geometric structures on Lie algebroids is studied. The notion of dynamical covariant derivative is introduced and a metric nonlinear connection is found in the more general case of Lie algebroids. We prove that the canonical nonlinear connection induced by a regular Lagrangian on a Lie algebroid is the unique co...