Deformations of Killing spinors on Sasakian and 3-Sasakian manifolds

We consider some natural infinitesimal Einstein deformations on Sasakian and 3-Sasakian manifolds. Some of these are infinitesimal deformations of Killing spinors and further some integrate to actual Killing spinor deformations. In particular, on 3-Sasakian 7 manifolds these yield infinitesimal Einstein deformations preserving 2, 1, or none of the 3 independent Killing spinors. Toric 3-Sasakian manifolds provide non-trivial examples with integrable deformation preserving precisely 2 Killing spinors. Thus the dimension of Killing spinors is not preserved under Einstein deformations but is only upper semi-continuous.Comment: 35 pages, 1 figur

Sasaki-Einstein 5-manifolds associated to toric 3-Sasaki manifolds

We give a correspondence between toric 3-Sasaki 7-manifolds S and certain toric Sasaki-Einstein 5-manifolds M. These 5-manifolds are all diffeomorphic to k#(S^2\times S^3), where k=2b_2(S)+1, and are given by a pencil of Sasaki embeddings of M in S and are given concretely by the zero set of a component of the 3-Sasaki moment map. It follows that there are infinitely many examples of these toric Sasaki-Einstein manifolds M for each odd b_2(M)>1. As an application of the proof of the above, we prove that the local deformation space of ASD structures on a compact toric ASD Einstein orbifold is given by Joyce ansatz conformal metrics.Comment: final corrections mad

Stability of Sasaki-extremal metrics under complex deformations

We consider the stability of Sasaki-extremal metrics under deformations of the complex structure on the Reeb foliation. Given such a deformation preserving the action of a compact subgroup of the automorphism group of a Sasaki-extremal structure, a sufficient condition is given involving the nondegeneracy of the relative Futaki invariant for the deformations to contain Sasaki-extremal structures. Deformations of Sasaki-Einstein metrics are also considered, where it suffices that the deformation preserve a maximal torus. As an application, new families of Sasaki-Einstein and Sasaki-extremal metrics are given on deformations of well known 3-Sasaki 7-manifolds.Comment: Added the obstruction to the existence of Sasaki structures under transversal complex deformations. 30 pages and 1 figur

Estimating economic and social welfare impacts of pension reform

This paper examines the impact of two effects of the pension reform package that the UK Government put forward in the May White Paper Security in retirement: the likely increase in the number of older people working due to a higher State Pension age and the likely rise in saving due to more people putting away money for retirement. The overall effect of changes to State Pension age and the introduction of personal accounts on UK incomes is likely to be in the range of 0.9 – 3.1 per cent. Although these numbers are relatively small proportions of the total economy, they represent significant sums. In terms of today’s economy, they would be worth around £11 – 38 billion. This paper also applies an innovative economic analysis to examine the scale of the increase in people’s wellbeing as a result of improved consumption smoothing. It finds that if people save for retirement through personal accounts, then generally their wellbeing will be enhanced.pension reform; consumption smoothing; social welfare

K\"{a}hler-Einstein metrics on strictly pseudoconvex domains

The metrics of S. Y. Cheng and S.-T. Yau are considered on a strictly pseudoconvex domains in a complex manifold. Such a manifold carries a complete K\"{a}hler-Einstein metric if and only if its canonical bundle is positive. We consider the restricted case in which the CR structure on $\partial M$ is normal. In this case M must be a domain in a resolution of the Sasaki cone over $\partial M$. We give a condition on a normal CR manifold which it cannot satisfy if it is a CR infinity of a K\"{a}hler-Einstein manifold. We are able to mostly determine those normal CR 3-manifolds which can be CR infinities. Many examples are given of K\"{a}hler-Einstein strictly pseudoconvex manifolds on bundles and resolutions.Comment: 30 pages, 1 figure, couple corrections, improved a couple example

The interplay between land use, travel behaviour and attitudes: a quest for causality.

Governments increasingly embrace land-use policies to promote sustainable travel behaviour. However, the causality of this relationship, and in particular the role of travel-related attitudes, is not clear. This thesis takes a longitudinal approach and explores the directions of causality. It shows that the built environment influences travel behaviour and that travel-related attitudes play an important intervening role. Implications for land-use policies and alignment with accompanying measures are discussed.TRAIL Thesis Series no. T2021/18, the Netherlands Research School TRAILTransport and Plannin