Search results for "bundle"

Classification and stable classification of manifolds: some examples

1984

Kähler manifolds with split tangent bundle

2006

( Varietes kahleriennes a fibre tangent scinde). - On etudie dans cet article les varietes kahleriennes compactes dont le fibre tangent se decompose en somme directe de sous-fibres. En particulier, on montre que si le fibre tangent se decompose en somme directe de sous-fibres en droites, alors la variete est uniformisee par un produit de courbes. Les methodes sont issues de la theorie des feuilletages de (co)dimension 1.

Subharmonic variation of the leafwise Poincar� metric

2003

Let X be a compact complex algebraic surface and let F be a holomorphic foliation, possibly with singularities, on X. On each leaf of F we put its Poincare metric (this will be defined below in more precise terms). We thus obtain a (singular) hermitian metric on the tangent bundle TF of F , and dually a (singular) hermitian metric on the canonical bundle KF = T ∗ F of F . The main aim of this paper is to prove that this metric on KF has positive curvature, in the sense of currents. Of course, the positivity of the curvature in the leaf direction is an immediate consequence of the definitions; the nontrivial fact is that the curvature is positive also in the directions transverse to the leaf…

Automatic orientation and 3D modelling from markerless rock art imagery

2013

This paper investigates the use of two detectors and descriptors on image pyramids for automatic image orientation and generation of 3D models. The detectors and descriptors replace manual measurements and are used to detect, extract and match features across multiple imagery. The Scale-Invariant Feature Transform (SIFT) and the Speeded Up Robust Features (SURF) will be assessed based on speed, number of features, matched features, and precision in image and object space depending on the adopted hierarchical matching scheme. The influence of applying in addition Area Based Matching (ABM) with normalised cross-correlation (NCC) and least squares matching (LSM) is also investigated. The pipel…

Some Afterthoughts on Hopfield Networks

1999

In the present paper we investigate four relatively independent issues, which complete our knowledge regarding the computational aspects of popular Hopfield nets. In Section 2 of the paper, the computational equivalence of convergent asymmetric and Hopfield nets is shown with respect to network size. In Section 3, the convergence time of Hopfield nets is analyzed in terms of bit representations. In Section 4, a polynomial time approximate algorithm for the minimum energy problem is shown. In Section 5, the Turing universality of analog Hopfield nets is studied. peerReviewed

Spectral rigidity and invariant distributions on Anosov surfaces

2014

This article considers inverse problems on closed Riemannian surfaces whose geodesic flow is Anosov. We prove spectral rigidity for any Anosov surface and injectivity of the geodesic ray transform on solenoidal 2-tensors. We also establish surjectivity results for the adjoint of the geodesic ray transform on solenoidal tensors. The surjectivity results are of independent interest and imply the existence of many geometric invariant distributions on the unit sphere bundle. In particular, we show that on any Anosov surface $(M,g)$, given a smooth function $f$ on $M$ there is a distribution in the Sobolev space $H^{-1}(SM)$ that is invariant under the geodesic flow and whose projection to $M$ i…

A New Early Cambrian Lobopod-Bearing Animal (Murero, Spain) and the Problem of the Ecdysozoan Early Diversification

2011

A new xenusian, Mureropodia apae gen. and sp. nov., is found in the lower Cambrian of the Murero Lagerstatte in the Cadenas Ibericas, NE Spain. In Mureropodia, the lobopod length/body width ratio reveals that this animal hardly was able to walk on the bottom surface. Possibly, it could use the limbs for anchoring the body to the substrate. A well-developed dermomuscular sac of circular and longitudinal muscular systems as well as probably retractile proboscis fit such an interpretation. The ground plan of the Xenusia includes a vermiform body; a proboscis or mouth cone; paired lobopods with claws; a cuticle displaying a repeated anatomical patterning; a straight digestive tract with termina…

On double Veronese embeddings in the Grassmannian G(1,N)

2004

We classify all the embeddings of P^n in a Grassmannian of lines G(1,N) such that the composition with Pl\"ucker is given by a linear system of quadrics of P^n.

Surfaces of minimal degree of tame representation type and mutations of Cohen–Macaulay modules

2017

We provide two examples of smooth projective surfaces of tame CM type, by showing that any parameter space of isomorphism classes of indecomposable ACM bundles with fixed rank and determinant on a rational quartic scroll in projective 5-space is either a single point or a projective line. For surfaces of minimal degree and wild CM type, we classify rigid Ulrich bundles as Fibonacci extensions. For the rational normal scrolls S(2,3) and S(3,3), a complete classification of rigid ACM bundles is given in terms of the action of the braid group in three strands.

Demonstration of a reef knot microfiber resonator.

2009

We propose a new way to realize a microfiber optical resonator by implementing the topology of a reef knot using two microfibers. We describe how this structure, which includes 4 ports and can serve as an add-drop filter, can be fabricated. Resonances in an all-silica reef knot are measured and good fits are obtained from a simple resonator model. We also show the feasibility of assembling a hybrid silica-chalcogenide reef knot structure.