We prove that polarised manifolds that admit a constant scalar curvature Kähler (cscK) metric satisfy a condition we call slope semistability. That is, we define the slope µ for a projective manifold and for each of its subschemes, and show that if X is cscK then µ(Z) ≤ µ(X) for all subschemes Z. This gives many examples of manifolds with Kähler classes which do not admit cscK metrics, such as ...

We prove that polarised manifolds that admit a constant scalar curvature Kähler (cscK) metric satisfy a condition we call slope semistability. That is, we define the slope µ for a projective manifold and for each of its subschemes, and show that if X is cscK then µ(Z) ≤ µ(X) for all subschemes Z. This gives many examples of manifolds with Kähler classes which do not admit cscK metrics, such as ...

A new infinite series of Einstein metrics is constructed explicitly on S2×S3, and the non-trivial S3-bundle over S2, containing infinite numbers of inhomogeneous ones. They appear as a certain limit of a nearly extreme 5-dimensional AdS Kerr black hole. In the special case, the metrics reduce to the homogeneous Einstein metrics studied by Wang and Ziller. We also construct an inhomogeneous Eins...

We prove that polarised manifolds that admit a constant scalar curvature Kähler (cscK) metric satisfy a condition we call slope semistability. That is, we define the slope µ for a projective manifold and for each of its subschemes, and show that if X is cscK then µ(Z) ≤ µ(X) for all subschemes Z. This gives many examples of manifolds with Kähler classes which do not admit cscK metrics, such as ...

To every real analytic Riemannian manifold M there is associated a complex structure on a neighborhood of the zero section in the real tangent bundle of M . This structure can be uniquely specified in several ways, and is referred to as a Grauert tube. We say that a Grauert tube is entire if the complex structure can be extended to the entire tangent bundle. We prove here that the complex manif...

We introduce the topcic of generalised geometry as an extension of differential geomentry on the bundle TM ⊕T ∗M . An algebraic structure is built that leads to the formation of the generalised tangent bundle. We place a generalised Riemannian metric on this space and show that it is compatible with the metric for a generalised Kähler structure. We investigate the nature of supersymmetric backg...

Stereo visual odometry has received little investigation in high altitude applications due to the generally poor performance of rigid stereo rigs at extremely small baseline-to-depth ratios. Without additional sensing, metric scale is considered lost and odometry is seen as effective only for monocular perspectives. This paper presents a novel modification to stereo based visual odometry that a...

We present a new approach for matching regular surfaces in a Riemannian setting. We use a Sobolev type metric on deformation vector fields which form the tangent bundle to the space of surfaces. In this article we compare our approach with the diffeomorphic matching framework. In the latter approach a deformation is prescribed on the ambient space, which then drags along an embedded surface. In...

With increasing globalization and the proliferation of communication technologies, more people are working in cross-functional, geographically distributed teams. Although trust is clearly an important ingredient in these collaborations, little is known about the challenges this new work and social environment creates for the development of trust. Different disciplinary perspectives, different r...

Let B be a fiber bundle with compact fiber F over a compact Riemannian n-manifold M. There is a natural Riemannian metric on the total space B consistent with the metric on M . With respect to that metric, the volume of a rectifiable section σ : M → B is the mass of the image σ(M) as a rectifiable n-current in B. For any homology class of sections of B, there is a mass-minimizing Cartesian curr...