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For a fat sub-Riemannian structure, we introduce three canonical Ricci curvatures in the sense of Agrachev–Zelenko–Li. Under appropriate bounds we prove comparison theorems for conjugate lengths, Bonnet–Myers type results and Laplacian comparison theorems for the intrinsic sub-Laplacian. As an application, we consider the sub-Riemannian structure of 3-Sasakian manifolds, for which we provide explicit curvature formulas. We prove that any complete 3-Sasakian structure of dimension
, has sub-Riemannian diameter bounded by
, a similar statement holds under additional Ricci bounds. These results are sharp for the natural sub-Riemannian structure on
of the quaternionic Hopf fibrations:
We present the first results of a comprehensive HST study of the star-formation history of Fornax dSph, based on WFPC2 imaging of 7 Fornax fields. Our observations reach the oldest main-sequence turnoffs, allowing us to address fundamental questions of dwarf galaxy evolution, such as the spatial variations in the stellar content, and whether the old stellar population is made up of stars formed in a very early burst or the result of a more continuous star formation.
We report on the recent developments of our long-term investigation of the near-IR luminosity-metallicity relation for dwarf irregular galaxies in nearby groups. A very well-defined relation is emerging from our observational database, and a preliminary discussion of its implications is given.
Results are presented on a study of the short period variable stars in the dwarf irregular galaxy NGC 6822. We observed an almost uniformly populated classical instability strip from the Horizontal Branch up to the Classical Cepheid region. The main goal we achieved from the analysis of the faint sample is the first detection of RR Lyrae stars in this galaxy.
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