Twistor theory of symplectic manifolds

This article is a contribution to the understanding of the geometry of the twistor space of a symplectic manifold. We consider the bundle $Z$ with fibre the Siegel domain Sp(2n,R)/U(n) existing over any given symplectic 2n-manifold M. Then, after recalling the construction of the almost complex structure induced on $Z$ by a symplectic connection on M, we study and find some specific properties of both. We show a few examples of twistor spaces, develop the interplay with the symplectomorphisms of M, find some results about a natural almost Hermitian structure on $Z$ and finally prove its n+1-holomorphic completeness. We end by proving a vanishing theorem about the Penrose transform.Comment: 34 page

On invariants of almost symplectic connections

We study the irreducible decomposition under Sp(2n, R) of the space of torsion tensors of almost symplectic connections. Then a description of all symplectic quadratic invariants of torsion-like tensors is given. When applied to a manifold M with an almost symplectic structure, these instruments give preliminary insight for finding a preferred linear almost symplectic connection on M . We rediscover Ph. Tondeur's Theorem on almost symplectic connections. Properties of torsion of the vectorial kind are deduced

Effects of trinexapae-ethyl on stoloon development in potted Patriot bermudagrass

A recent technique developed for establishment of warm season turfgrasses is based on the transplant of single plug plantlets pre-rooted in the nursery. Plantlets are obtained from one-node sprigs about 2 cm long derived from stolon fragmentation. Usually, stolons must be cut several times to obtain sprigs of the right length because of overly long internodes. In the present study, potted plants of Patriot bermudagrass grown in the nursery were treated with trinexa-pac-ethyl (TE) at the rates 0.1, 0.2, 0.4 and 0.8 kg a.i. ha-1. TE application was aimed at obtaining internode shortening in order to facilitate the stolon division practice. In fact, TE-treated plants showed a decrease in the average length of internodes with respect to control at any applied rate. Nevertheless, the lowest rate applied (0.1 kg a.i. ha-1) did not assure a prolonged effect while the highest rate (0.8 kg a.i. ha-1) caused a decrease in the yield of sprigs. Therefore, our results suggest that TE may be advantageously used and at rates of 0.2-0.4 kg a.i. ha-1 to control stolon development of Patriot bermudagrass for nursery purposes