on a finsler manifold, we define conformal vector fields and their complete lifts and prove that incertain conditions they are homothetic.

We construct some lift of an almost complex structure to the cotangent bundle, using a connection on the base manifold. This unifies the complete lift defined by I.Satô and the horizontal lift introduced by S.Ishihara and K.Yano. We study some geometric properties of this lift and its compatibility with symplectic forms on the cotangent bundle.

An n-lift of a graph K, is a graph with vertex set V (K)× [n] and for each edge (i, j) ∈ E(K) there is a perfect matching between {i} × [n] and {j} × [n]. If these matchings are chosen independently and uniformly at random then we say that we have a random n-lift. We show that there are constants h1, h2 such that if h ≥ h1 then a random n-lift of the complete graph Kh is hamiltonian whp and if ...

In the present paper, we study complete and vertical lifts of tensor fields from a smooth manifoldM to its Weil bundle TM defined by a Frobenius Weil algebra A. For a Poisson manifold (M,w), we show that the complete lift w and the vertical lift w of the Poisson tensor w are Poisson tensors on TM and establish their properties. We prove that the complete and the vertical lifts induce homomorphi...