Local classification and examples of an important class of paracontact metric manifolds

We study paracontact metric $(\kappa,\mu)$-spaces with $\kappa=-1$, equivalent to $h^2=0$ but not $h=0$. In particular, we will give an alternative proof of Theorem 3.2 of [11] and present examples of paracontact metric $(-1,2)$-spaces and $(-1,0)$-spaces of arbitrary dimension with tensor $h$ of every possible constant rank. We will also show explicit examples of paracontact metric $(-1, \mu)$-spaces with tensor $h$ of non-constant rank, which were not known to exist until now.Comment: 9 page

Paracontact metric manifolds without a contact metric counterpart

We study non-paraSasakian paracontact metric $(\kappa,\mu)$-spaces with $\kappa=-1$ (equivalent to $h^2=0$ but $h\neq0$). These manifolds, which do not have a contact geometry counterpart, will be classified locally in terms of the rank of $h$. We will also give explicit examples of every possible constant rank of $h$.Comment: 12 pages; several corrections have been made in this versio

Paracontact metric structures on the unit tangent sphere bundle

Starting from $g$-natural pseudo-Riemannian metrics of suitable signature on the unit tangent sphere bundle $T_1 M$ of a Riemannian manifold $(M,\langle,\rangle)$, we construct a family of paracontact metric structures. We prove that this class of paracontact metric structures is invariant under $\mathcal D$-homothetic deformations, and classify paraSasakian and paracontact $(\kappa,\mu)$-spaces inside this class. We also present a way to build paracontact $(\kappa,\mu)$-spaces from corresponding contact metric structures on $T_1 M$.Comment: 21 page

Una ordenación adaptada a la protección social de la maternidad-paternidad por subrogación

The gestation surrogate has been demanding a regulatory space within our legal system that seems to advance towards its concretion in recent times. In terms of Social Protection of maternity-paternity situations arising from it, which is the subject of the present investigation, its management is still limited and derives from sources nor properly normative. However, this study builds a kind of legal regime, based on this arrangement, but also with attention to different elements arranged for other contingencies of the System.La gestación subrogada viene reclamando un espacio de regulación dentro de nuestro ordenamiento jurídico que parece avanzar hacia su concreción en fechas recientes. En materia de Protección Social de las situaciones de maternidad-paternidad derivadas de ella, que es el objeto de la presente investigación, su ordenación es aún limitada y dimana de fuentes no propiamente normativas. Con todo, en este estudio se construye una suerte de régimen jurídico, sobre la base de dicha ordenación, pero también con atención a elementos distintos dispuestos para otras contingencias del Sistema

A way of integrating technological tools into teacher training

This paper presents an experience of didactic innovation and its impact on the learning of teacher training students who took a course on School Organization. With the innovation described here we attempted to use technological tools with our students as a positive stimulus during the teaching and learning processes which would enable them to learn more effectively. Students considered this experience as positive and they got better marks than students in the previous academic year