Stenzel's Ricci-flat Kaehler metrics are not projectively induced

We investigate the existence of a holomorphic and isometric immersion in the complex projective space for the complete Ricci-flat Kaehler metrics constructed by M. B. Stenzel on the cotangent bundle of a compact, rank one, globally symmetric space.Comment: 8 page

Canonical metrics on Cartan--Hartogs domains

In this paper we address two problems concerning a family of domains M_{\Omega}(\mu) \subset \C^n, called Cartan-Hartogs domains, endowed with a natural Kaehler metric $g(\mu)$. The first one is determining when the metric $g(\mu)$ is extremal (in the sense of Calabi), while the second one studies when the coefficient $a_2$ in the Engli\v{s} expansion of Rawnsley $\epsilon$-function associated to $g(\mu)$ is constant.Comment: 13 page

On the convergence of the Sasaki J-flow

This paper investigates the $C^\infty$-convergence of the Sasaki $J$-flow. The result is applied to prove a lower bound for the $K$-energy map in the Sasakian context.Comment: 15 page

A note on the coefficients of Rawnsley's epsilon function of Cartan-Hartogs domains

We extend a result of Z. Feng and Z. Tu by showing that if one of the coefficients $a_j$, $2\leq j\leq n$, of Rawnlsey's epsilon function associated to a $n$-dimensional Cartan-Hartogs domain is constant, then the domain is biholomorphically equivalent to the complex hyperbolic space.Comment: 6 p

K\"ahler immersions of K\"ahler manifolds into complex space forms

The study of K\"ahler immersions of a given real analytic K\"ahler manifold into a finite or infinite dimensional complex space form originates from the pioneering work of Eugenio Calabi [10]. With a stroke of genius Calabi defines a powerful tool, a special (local) potential called diastasis function, which allows him to obtain necessary and sufficient conditions for a neighbourhood of a point to be locally K\"ahler immersed into a finite or infinite dimensional complex space form. As application of its criterion, he also provides a classification of (finite dimensional) complex space forms admitting a K\"ahler immersion into another. Although, a complete classification of K\"ahler manifolds admitting a K\"ahler immersion into complex space forms is not known, not even when the K\"ahler manifolds involved are of great interest, e.g. when they are K\"ahler-Einstein or homogeneous spaces. In fact, the diastasis function is not always explicitely given and Calabi's criterion, although theoretically impeccable, most of the time is of difficult application. Nevertheless, throughout the last 60 years many mathematicians have worked on the subject and many interesting results have been obtained. The aim of this book is to describe Calabi's original work, to provide a detailed account of what is known today on the subject and to point out some open problems.Comment: 116 page

Isometric immersions of locally conformally Kaehler manifolds

We investigate isometric immersions of locally conformally Kaehler metrics into Hopf manifolds. In particular, we study Hopf-induced metrics on compact complex surfaces.Comment: 20 pages. Revised version with main corrections to Prop. 3.4, Prop. 3.6 and Prop. 3.9 (and Th. 1.1 consequently

Lichens and their importance for the monitoring of environmental changes in Southern Africa : with special reference to soil-inhabiting lichens.

Lichens are the object of investigation within the framework of the BIOTA Southern Africa project, subproject S04 (http://www.biota-africa.org). This interdisciplinary research project, installed in 2000, focuses on the analysis of biodiversity and its changes along climatic and vegetation gradients (transects) in Namibia and in the Republic of South Africa. In the context of this project, studies on the diversity of lichens are carriedout. Special reference is given to the monitoring of lichens growing on soil, which form the so called biological soil crusts.Lichen diversity is assessed and analysed with respect to its spatial and temporal changes. These are related to various abioticand biotic factors such as climate, soil features and land use. The indicator value of certain terricolouslichen taxaand/or lichen groups (communities) is investigated for the study area, and it is intended to use itin a future long-term monitoring programme in the region. In this brochure, we whish to explain what lichens are, how do they live and where do they grow, and why they are so important as bioindicatorsin arid and semi-arid areas of the world. The activities of the S04 subproject along the BIOTA transect are described, as well as the methods used for monitoring environmental changes in Southern Africa using soil-inhabiting lichens

Note sull'apprendimento nella teoria di Leopardi

Leopardi examines very carefully the life of the mind and, particularly, the learning of new contents. The crucial point is the concept of assuefare (to get accustomed), a process conceived as a slow acquisition of new mental habits and shapes. This procedure results in extraordinary outcomes in every realms of life. Leopardi's reflection represents an important contribution to didactics and pedagogy, while emphasizing personal will and practice