Search results for "GRAVITATION"

Inflection points and topology of surfaces in 4-space

2000

We consider asymptotic line fields on generic surfaces in 4-space and show that they are globally defined on locally convex surfaces, and their singularities are the inflection points of the surface. As a consequence of the generalized Poincare-Hopf formula, we obtain some relations between the number of inflection points in a generic surface and its Euler number. In particular, it follows that any 2-sphere, generically embedded as a locally convex surface in 4-space, has at least 4 inflection points.

ASYMPTOTIC CURVES ON SURFACES IN ℝ5

2008

We study asymptotic curves on generically immersed surfaces in ℝ5. We characterize asymptotic directions via the contact of the surface with flat objects (k-planes, k = 1 - 4), give the equation of the asymptotic curves in terms of the coefficients of the second fundamental form and study their generic local configurations.

On the number of singularities of a generic surface with boundary in a 3-manifold

1998

Convergent transformations into a normal form in analytic Hamiltonian systems with two degrees of freedom on the zero energy surface near degenerate …

2004

We study an analytic Hamiltonian system with two degrees of freedom, having the origin as an elliptic singularity. We assume that the full Birkhoff normal form exists and is divisible by its quadratic part, being indefinite. We show that under the Bruno condition and under the restriction to the zero energy surface, a real analytic transformation into a normal form exists. Such a normal form coincides with the restriction of the Birkhoff normal form to the zero energy surface up to an order as large as we want.

On stability of generic subriemannian caustic in the three-space

2000

Abstract The singularities of exponential mappings in subriemannian geometry are interesting objects, that are already non-trivial at the local level, contrarily to their Riemannian analogs. The simplest case is the three-dimensional contact case. Here we show that the corresponding generic caustics have moduli at the origin, and the first module that occurs has a simple geometric interpretation. On the contrary, we prove a stability result of the “big wave front”, that is, of the graph of the multivalued arclength function, reparametrized in a certain way. This object is a three-dimensional surface, which has also the natural structure of a wave front. The projection on the three-dimension…

Tree Singularities: Limits, Series and Stability

2013

A tree singularity is a surface singularity that consists of smooth components, glued along smooth curves in the pattern of a tree. Such singularities naturally occur as degenerations of certain rational surface singularities. To be more precise, they can be considered as limits of certain series of rational surface singularities with reduced fundamental cycle. We introduce a general class of limits, construct series deformations for them and prove a stability theorem stating that under the condition of finite dimensionality of T 2 the base space of a semi-universal deformation for members high in the series coincides up to smooth factor with the “base space of the limit”. The simplest tree…

Preliminary results of a geomorphological and DInSAR characterization of a recently identified Deep-Seated Gravitational Slope Deformation in Sicily …

2019

The study is part of a larger project that involves the analysis of recently identified Deep-Seated Gravitational Slope Deformation (DSGSD) in Sicily which have been sub-divided according to the geological framework in light of the new geological data about the regional setting. Here are presented the first results of a multidisciplinary study of a DSGSD recently identify in Mount San Calogero area (Northern Sicily). The study was performed by means of different approaches including conventional methods (field surveys) and the Differential Interferometry Synthetic Aperture Radar (DInSAR) technique. The geological and geomorphological analyses were carried out to investigate slopes dynamic, …

Open data from the first and second observing runs of advanced LIGO and advanced Virgo

2021

Abbot, Rich, et al. (Virgo and MAGIC Collaboration)

On C1 robust singular transitive sets for three-dimensional flows

1998

Abstract The main goal of this paper is to study robust invariant transitive sets containing singularities for C 1 flows on three-dimensional compact boundaryless manifolds: they are partially hyperbolic with volume expanding central direction. Moreover, they are either attractors or repellers. Robust here means that this property cannot be destroyed by small C 1 -perturbations of the flow.

Advanced Virgo Status

2015

Abstract The detection of a gravitational wave signal in September 2015 by LIGO interferometers, announced jointly by LIGO collaboration and Virgo collaboration in February 2016, opened a new era in Astrophysics and brought to the whole community a new way to look at - or “listen” to - the Universe. In this regard, the next big step was the joint observation with at least three detectors at the same time. This configuration provides a twofold benefit: it increases the signal-to-noise ratio of the events by means of triple coincidence and allows a narrower pinpointing of GW sources, and, in turn, the search for Electromagnetic counterparts to GW signals. Advanced Virgo (AdV) is the second ge…