The canonical 8-form on manifolds with holonomy group Spin(9)

An explicit expression of the canonical 8-form on a Riemannian manifold with a Spin(9)-structure, in terms of the nine local symmetric involutions involved, is given. The list of explicit expressions of all the canonical forms related to Berger's list of holonomy groups is thus completed. Moreover, some results on Spin(9)-structures as G-structures defined by a tensor and on the curvature tensor of the Cayley planes, are obtained

Nuevos taxones para el Rif occidental. II

New taxa from W Rif. II.Palabras clave. Flora, corología, Rif, N de Marruecos.Key words. Flora, chorology, Rif, Northern Morocco

Lagrangian reductive structures on gauge-natural bundles

A reductive structure is associated here with Lagrangian canonically defined conserved quantities on gauge-natural bundles. Parametrized transformations defined by the gauge-natural lift of infinitesimal principal automorphisms induce a variational sequence such that the generalized Jacobi morphism is naturally self-adjoint. As a consequence, its kernel defines a reductive split structure on the relevant underlying principal bundle.Comment: 11 pages, remarks and comments added, this version published in ROM

On the cohomology of some exceptional symmetric spaces

This is a survey on the construction of a canonical or "octonionic K\"ahler" 8-form, representing one of the generators of the cohomology of the four Cayley-Rosenfeld projective planes. The construction, in terms of the associated even Clifford structures, draws a parallel with that of the quaternion K\"ahler 4-form. We point out how these notions allow to describe the primitive Betti numbers with respect to different even Clifford structures, on most of the exceptional symmetric spaces of compact type.Comment: 12 pages. Proc. INdAM Workshop "New Perspectives in Differential Geometry" held in Rome, Nov. 2015, to appear in Springer-INdAM Serie

On the explicit expressions of the canonical 8-form on Riemannian manifolds with Spin (9) holonomy

6 pags. 1991 Mathematics Subject Classification. Primary 53C29, Secondary 53C27.Two explicit expressions of the canonical 8-form on a Riemannian manifold with holonomy group Spin(9) have been given: One by the present authors and another by Parton and Piccinni. The relation between these two expressions is obtained. Moreover, it is shown that they are different only from a combinatorial viewpoint.The first author has been supported by DGI (Spain) Project MTM2013-46961-P..Peer reviewe

Análisis polínico de mieles en las regiones de Ouazzane y Costa Atlántica (Noroeste de Marruecos)

Análisis polínico de mieles en las regiones de Ouazzane y Costa Atlántica (Noroeste de Marruecos). Se ha realizado el análisis microscópico de 13 muestras de miel de las regiones de Ouazzane y Costa Atlántica. Las muestras fueron proporcionadas directamente por los apicultores, en su mayoría aficionados. Los resultados reflejan que el néctar de las flores es la principal fuente de miel en el territorio y que siete de las muestras son pobres polinicamente, con 4.600-47.800 GP (Clase I y II de Maurizio), dos muestras presentan una riqueza media, con 189.000-209.700 GP (Clase III), y cuatro son ricas o muy ricas, con 872.000-2.950.000 GP (Clases IV y V). Se han identificado 63 taxones por el análisis microscópico, resultando seis de las mieles monoflorales: dos de Eucalyptus sp., dos de Lythrum sp., una de Leucojum sp. y una de Citrus sp

Ruled surfaces in 33-dimensional Riemannian manifolds

In this work ruled surfaces in $3$-dimensional Riemannian manifolds are studied. We determine the expression for the extrinsic and sectional curvature of a parametrized ruled surface, where the former one is shown to be non-positive. We also quantify the set of ruling vector fields along a given base curve which allow to define a relevant reference frame along it and that we refer to as \emph{Sannia}. The fundamental Theorem of existence and equivalence of Sannia ruled surfaces in terms of a system of invariants is given. The second part of the article tackles the concept of striction curve, which is proven to be the set of points where the so-called \emph{Jacobi evolution function} vanishes on a ruled surface. This provides independent proofs for their existence and uniqueness in space forms, and to disprove its existence or uniqueness in some other cases.Comment: 22 page