Curvature properties of ϕ\phi-null Osserman Lorentzian S\mathcal{S}-manifolds

We expound some results about the relationships between the Jacobi operators with respect to null vectors on a Lorentzian $\mathcal{S}$-manifold $M$ and the Jacobi operators with respect to particular spacelike unit vectors on $M$. We study the number of the eigenvalues of such operators in a $\phi$-null Osserman Lorentzian $\mathcal{S}$-manifold, under suitable assumptions on the dimension of the manifold. Then, we generalize a curvature characterization, previously obtained by the first author for Lorentzian $\phi$-null Osserman $\mathcal{S}$-manifolds with exactly two characteristic vector fields, to the case of those with an arbitrary number of characteristic vector fields.Comment: 15 pages; signs corrected on page 8, reference adde

MasakhaPOS: Part-of-Speech Tagging for Typologically Diverse African languages

In this paper, we present AfricaPOS, the largest part-of-speech (POS) dataset for 20 typologically diverse African languages. We discuss the challenges in annotating POS for these languages using the universal dependencies (UD) guidelines. We conducted extensive POS baseline experiments using both conditional random field and several multilingual pre-trained language models. We applied various cross-lingual transfer models trained with data available in the UD. Evaluating on the AfricaPOS dataset, we show that choosing the best transfer language(s) in both single-source and multi-source setups greatly improves the POS tagging performance of the target languages, in particular when combined with parameter-fine-tuning methods. Crucially, transferring knowledge from a language that matches the language family and morphosyntactic properties seems to be more effective for POS tagging in unseen languages

Pseudoinversion of degenerate metrics

Let (M,g) be a smooth manifold M endowed with a metric g. A large class of differential operators in differential geometry is intrinsically defined by means of the dual metric g∗ on the dual bundle TM∗ of 1-forms on M. If the metric g is (semi)-Riemannian, the metric g∗ is just the inverse of g. This paper studies the definition of the above-mentioned geometric differential operators in the case of manifolds endowed with degenerate metrics for which g∗ is not defined. We apply the theoretical results to Laplacian-type operator on a lightlike hypersurface to deduce a Takahashi-like theorem (Takahashi (1966)) for lightlike hypersurfaces in Lorentzian space ℝ1n+2

Lightlike Einstein's hypersurfaces in Lorentzian manifolds with constant curvature

Consiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7 , Rome / CNR - Consiglio Nazionale delle RichercheSIGLEITItal