Genericity of Nondegenerate Critical Points and Morse Geodesic Functionals

We consider a family of variational problems on a Hilbert manifold parameterized by an open subset of a Banach manifold, and we discuss the genericity of the nondegeneracy condition for the critical points. Using classical techniques, we prove an abstract genericity result that employs the infinite dimensional Sard-Smale theorem, along the lines of an analogous result of B. White [29]. Applications are given by proving the genericity of metrics without degenerate geodesics between fixed endpoints in general (non compact) semi-Riemannian manifolds, in orthogonally split semi-Riemannian manifolds and in globally hyperbolic Lorentzian manifolds. We discuss the genericity property also in stationary Lorentzian manifolds.

An existence theorem for G-structure preserving affine immersions

We prove an existence result for local and global G-structure preserving affine immersions between affine manifolds. Several examples are discussed in the context of Riemannian and semi-Riemannian geometry, including the case of isometric immersions into Lie groups endowed with a left-invariant metric, and the case of isometric immersions into products of space forms.

A Survey of Fungal Contamination on Books in Public Libraries with Mechanical and Natural Ventilation

Libraries are very propitious environments for the growth of fungi. The great concentration of organic material available for these microorganisms, and often with the lack of adequate ventilation or climate control, would favour this situation. This study was conducted in 2003 to determine the predominant genera of fungi in public libraries by a survey of fungi contaminating the upper surface of books, with and without air conditioning in the city of Sao Paulo, Brazil, in the winter and summer, during the respective periods with high and low levels of airborne fungi in that city. Six libraries were chosen, located on the campus of the University of Sao Paulo, three of them with air conditioning and the other three with natural ventilation. In these six libraries, 31 genera of fungi were identified in total. The genera and frequency of contaminant fungi recovered differed significantly between the libraries with and without air conditioning and in the samples collected in the summer as opposed to the winter. Cladosporium was the most frequent in the libraries with and without air conditioning, and in the winter. Aspergillus was isolated more often in the summer.