841 research outputs found
A metric property of umbilic points
In the space of cubic forms of surfaces, regarded as a
-space and endowed with a natural invariant metric, the ratio of the volumes
of those representing umbilic points with negative to those with positive
indexes is evaluated in terms of the asymmetry of the metric, defined here. A
connection of this ratio with that reported by Berry and Hannay (1977) in the
domain of Statistical Physics, is discussed.Comment: 8 pages, 1 figur
The Minimal Geometric Deformation Approach: a brief introduction
We review the basic elements of the Minimal Geometric Deformation approach in
details. This method has been successfully used to generate brane-world
configurations from general relativistic perfect fluid solutions.Comment: Brief review; minor corrections; references adde
Anisotropic solutions by gravitational decoupling
We investigate the extension of isotropic interior solutions for static
self-gravitating systems to include the effects of anisotropic spherically
symmetric gravitational sources by means of the gravitational decoupling
realised via the minimal geometric deformation approach. In particular, the
matching conditions at the star surface with the outer Schwarzschild space-time
are studied in great details, and we describe how to generate, from a single
physically acceptable isotropic solution, new families of anisotropic solutions
whose physical acceptability is also inherited from their isotropic parent.Comment: 20 pages, 4 figures; references and typos corrected; final version to
match the EPJC versio
A causal Schwarzschild-de Sitter interior solution by gravitational decoupling
We employ the minimal geometric deformation approach to gravitational
decoupling (MGD- decoupling) in order to build an exact anisotropic version of
the Schwarzschild interior solution in a space-time with cosmological constant.
Contrary to the well-known Schwarzschild interior, the matter density in the
new solution is not uniform and possesses subluminal sound speed. It therefore
satisfies all standard physical requirements for a candidate astrophysical
object.Comment: 15 pages, 6 figure
Canard Cycles and Poincar\'e Index of Non-Smooth Vector Fields on the Plane
This paper is concerned with closed orbits of non-smooth vector fields on the
plane. For a subclass of non-smooth vector fields we provide necessary and
sufficient conditions for the existence of canard kind solutions. By means of a
regularization we prove that the canard cycles are singular orbits of singular
perturbation problems which are limit periodic sets of a sequence of limit
cycles. Moreover, we generalize the Poincar\'e Index for non-smooth vector
fields.Comment: 20 pages, 25 figure
Curvatures of conflict surfaces in Euclidean 3-space
This article extends to three dimensions results on the curvature of the conflict curve for pairs of convex sets of the plane established by Siersma In the present case a conflict surface arises equidistant from the given convex sets The Gaussian Mean Curvatures and the location of Umbilic Points on the conflict surface are determined here Initial results on the Darbouxian type of Umbilic Points on conict surfaces are also established The results are expressed in terms of the principal directions and on the curvatures of the borders of the given convex set
Structural Stability of Asymptotic Lines on Surfaces Immersed in R3
AbstractIn this paper are studied immersions of surfaces into to R3 whose nets of asymptotic lines are topologically undisturbed under small perturbations of the immersion. These immersions are called structurally asymptotic stable. Sufficient conditions to belong to this class are established here. These conditions focus on the stable patterns around parabolic points, parabolic separatrix connections, periodic asymptotic lines (including those that intercept the parabolic lines) as well the exclusion of recurrent asymptotic lines. The class of immersions that are structurally stable in this sense is open in the C5-topology
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