The uniformly accelerated motion in General Relativity from a geometric point of view

The notion of a uniformly accelerated rectilinear motion of an observer in a general spacetime is analysed in detail. From a geometric viewpoint, a uniformly accelerated observer may be seen as a Lorentzian circle. Finally, we find geometric assumptions to ensure that an inextensible uniformly accelerated rectilinear observer does not disappear in a finite proper time

Hipersuperficies isoparamétricas en el espacio hiperbólico complejo CHn

Se presenta la clasificación de las hipersuperficies isoparamétricas del espacio hiperbólico complejo CHn, siguiendo el trabajo realizado en J. C. Díaz-Ramos, M. Domínguez-Vázquez, V. Sanmartín-López, Isoparametric hypersurfaces in complex hyperbolic spaces, Adv. Math. 314 (2017), 756-805.Xunta de GaliciaPrograma de Formación del Profesorado UniversitarioFundación Barrié de la Maz

Diferenciales cuadráticas holomorfas en superficies lineales de Weingarten elípticas

En este trabajo definimos una diferencial de Hopf para superficies lineales de Weingarten que además satisfacen una relación de tipo elíptico al ser vistas como grafo sobre sus planos tangentes. Como consecuencia damos un teorema de unicidad de tipo Hopf.Ministerio de Economía y Competitivida

Totally umbilic null hypersurfaces in generalized Robertson-Walker spaces

Using a correspondence between totally umbilic null hypersurfaces in generalized Robertson-Walker spaces and twisted decompositions of the fibre we show that nullcones are the unique totally umbilic null hypersurfaces in the closed Friedmann Cosmological model and a uniqueness result for dual pairs of totally umbilic null hypersurfaces in Reissner-Nordström and De Sitter-Schwarzschild spacetimes.Junta de AndalucíaMinisterio de Economía y CompetitividadFondo Europeo de Desarrollo Regiona

Lagrangian translators under mean curvature flow

We provide a new construction of Lagrangian surfaces in C2 in terms of two planar curves. When we take such curves as appropriate solutions of the curve shortening problem, including self-shrinking and self-expanding curves or spirals, we will obtain translating solitons which generalize the Joyce, Lee and Tsui ones in dimension two D. Joyce, Y.-I. Lee, and M.-P. Tsui. Self-similar solutions and translating solitons for Lagrangian mean curvature flow. J. Differential Geom. 84 (2010), no. 1, 127-161. Finally, we characterize locally all examples in terms of an analytical condition on the Hermitian product of the position vector of the immersion and the translating vector that allows us separation of variables. As a consequence we get the classification of the Hamiltonian stationary Lagrangian translating solitons for Lagrangian mean curvature flow in complex Euclidean plane. This work is based in I. Castro and A. M. Lerma. Translating solitons for Lagrangian mean curvature flow in complex Euclidean plane. Internat. J. Math. 23 (2012), no. 10, 1250101-1-1250101-16.Ministerio de Economía y CompetitividadFondo Europeo de Desarrollo RegionalJunta de Andalucí

Causal properties of doubly warped spacetimes

In this talk we will describe the characterization of the chronological relation on doubly warped product spacetimes of the form (a, b) × M1 × M2 with Lorentzian metric g = −dt2 + α1g1 + α2g2, and we will discuss when these spacetimes are causally continuos and causally simple. This talk is based on the first section of L. Aké, J.L. Flores and J. Herrera, Causality and c-completion of doubly warped spacetimes, available at arXiv:1709.00234.Ministerio de Economía y CompetitividadFondo Europeo de Desarrollo RegionalConsejo Nacional de Ciencia y Tecnología (México

Contractions of certain Lie algebras

This communication is focused on the study of contractions of certain types of Lie algebras of low dimension, in order to address the implementation of the results to certain physical concepts, such as the boundary process by which quantum mechanics contracts to classical mechanics. To do this, we consider in the first place the contractions of filiform Lie algebras, which were introduced by M. Vergné in 1966, by using the psi and phi invariant functions, introduced in 2008 by Hrivnák and Novotny. These functions are also dealt with other types of algebra, as Heisenberg algebras among others, and we study the existing contractions between these algebras.Ministerio de Ciencia e InnovaciónJunta de Andalucí

Una aproximación geométrica a la aerodinámica de curvas y superficies

En este trabajo presentamos una primera aproximación al estudio geométrico de la aerodinámica de curvas y superficies. En primer lugar, motivaremos el estudio a partir de situaciones concretas y ejemplos físicos, para después adaptar el método de aproximación normal de curvas y superficies regulares, mediante curvas y superficies de Bézier, introducido por A. Carriazo, M. C. Márquez y H. Ugail. Concluiremos presentando ejemplos gráficos.Plan Andaluz de Investigación (Junta de Andalucía