Concavity and rigidity in non-negative curvature

This is a significantly improved version with new applications. We show that there are many cohomogeneity one manifolds which do not admit an analytic invariant metric with non-negative sectional curvature, although they do have a smooth one. In particular, there are no invariant metric with positive curvature

Totally geodesic orbits of isometries

We study cohomogeneity one Riemannian manifolds and we establish some simple criterium to test when a singular orbit is totally geodesic. As an application, we classify compact, positively curved Riemannian manifolds which are acted on isometrically by a non semisimple Lie group with an hypersurface orbit.Comment: 13 page

The church of St. Saturnino in Cagliari, Sardinia, reading the levels of history through the use of digital survey and the petrophysical study of materials

The most ancient church in Cagliari is dedicated to Saint Saturno (commonly named Saint Saturnino), the first indications about this church came from the sixth century, but the building arrived to our time is only a part of the original one and it rises over the ruins of previous structures, inside a a walled area with the presence of a Palaeo-Christian necropolis. The original Greek cross plan with a transept and a semi-spherical dome; has seen meaningful transformations in time, with the partial destruction of large parts of the building. All the four arms had a nave and two aisles, but the current church consists only of the dome-covered area and of the eastern arm, with a nave and two aisles. The whole church shows very interesting parts coming from previous architectures of the Roman age, a rich catalog of rich materials and details. In summer 2013, a collaboration between the Departments of Chemical and Geological Sciences from Cagliari and the one of Architecture from Florence brought to the realization of a detailed study about this ancient church. The whole building and its surrounding area were surveyed with the following methods: photography, 3D Laser Scanner for the whole interior and exterior parts, 3D photogrammetry of a selected set of stone surface samples, direct sampling of representative rocks for geochemical and petrophysical analysis. All data were then treated and analyzed to deepen the knowledge about the most meaningful aspects of different construction techniques and use of materials, provenance of raw materials, stone and structure alterations. As the result, a base was created to read common behaviors, design choices, recursive constructive solutions, and the “models” guiding the ancient intentions. This contribution will present the progress state of this research and its results

Non-negative curvature obstructions in cohomogeneity one and the Kervaire spheres

In contrast to the homogeneous case, we show that there are compact cohomogeneity one manifolds, that do not support invariant metrics of non-negative sectional curvature. In fact we exhibit infinite families of such manifolds including the exotic Kervaire spheres. Such examples exist for any codimension of the singular orbits except for the case where both are equal to two, where existence of non-negatively curved metrics is known.Comment: 10 page

Positively curved homogeneous metrics on spheres

We examine homogeneous metrics on spheres and determine which ones have positive sectional curvature. The answer is subtle and surprisingly difficult to prove. In some cases we also determine their pinching constants. This completes the classification of all homogeneous metrics with positive curvature (apart from one special Aloff Wallach space where the set of homogeneous metrics is too large).Comment: 17 pages, 10 figure

Reflections about the mute complaint of anorexia

Considerando-se que o caráter primordial do significante se exerce em relação ao sujeito, buscamos compreender o sujeito anoréxico através da investigação do significante "corpo". O material foi constituído por uma entrevista semi-estruturada, de noventa minutos, realizada com uma paciente diagnosticada como anoréxica. A análise dos dados foi qualitativa, seguindo a análise do discurso "francesa" e a psicanálise lacaniana, e permitiu constatar que o significante "corpo" atrelou-se a "peso" e "alimentação" na mesma cadeia discursiva. Desse modo, essa cadeia significante veio compor a ordem da identidade e da alteridade do sujeito, sob a égide do (sem) controle. Concluímos que a queixa muda da anoréxica, que se materializou como a recusa alimentar, era dirigida ao Outro como uma tentativa de alcançar sua alteridade.Taking into consideration that the main characteristic of the signifier is practiced in relation to the subject, we attempted to understand the anorexic subject through an investigation of the specific signifier "body". The study material was formed by a ninety minutes semi-structured interview with a patient diagnosed as anorexic. Data analysis was qualitative, following the "French" discourse analysis and Lacanian psychoanalysis. The analysis indicated that the signifier "body" was linked to "weight" and "feeding" in the same discursive chain. Thus, this significant chain established the order of identity and alterity, governed by (lack of) control. The conc1usion is that the anorexic´s silent complaint, materialized through a refusal to eat, is directed at the Other in an attempt to attain alterity