Designed for intermediate graduate studies, this text will broaden students' core knowledge of differential geometry providing foundational material to relevant topics in classical differential geometry. The method of moving frames, a natural means for discovering and proving important results, provides the basis of treatment for topics discussed. Its application in many areas helps to connect the various geometries and to uncover many deep relationships, such as the Lawson correspondence. The nearly 300 problems and exercises range from simple applications to open problems. Exercises are embedded in the text as essential parts of the exposition. Problems are collected at the end of each chapter; solutions to select problems are given at the end of the book. Mathematica®, MatlabTM, and Xfig are used to illustrate selected concepts and results. The careful selection of results serves to show the reader how to prove the most important theorems in the subject, which may become the foundation of future progress. The book pursues significant results beyond the standard topics of an introductory differential geometry course. A sample of these results includes the Willmore functional, the classification of cyclides of Dupin, the Bonnet problem, constant mean curvature immersions, isothermic immersions, and the duality between minimal surfaces in Euclidean space and constant mean curvature surfaces in hyperbolic space. The book concludes with Lie sphere geometry and its spectacular result that all cyclides of Dupin are Lie sphere equivalent. The exposition is restricted to curves and surfaces in order to emphasize the geometric interpretation of invariants and other constructions. Working in low dimensions helps students develop a strong geometric intuition. Aspiring geometers will acquire a working knowledge of curves and surfaces in classical geometries. Students will learn the invariants of conformal geometry and how these relate to the invariants of Euclidean, spherical, and hyperbolic geometry. They will learn the fundamentals of Lie sphere geometry, which require the notion of Legendre immersions of a contact structure. Prerequisites include a completed one semester standard course on manifold theory.
La Grande Italia traces the history of the myth of the nation in Italy along the curve of its rise and fall throughout the twentieth century. Starting with the festivities for the fiftieth anniversary of the unification of Italy in 1911 and ending with the centennial celebrations of 1961, Emilio Gentile describes a dense sequence of events: from victorious Italian participation in World War I through the rise and triumph of Fascism to Italy's transition to a republic. Gentile's definition of "Italians" encompasses the whole range of political, cultural, and social actors: Liberals and Catholics, Monarchists and Republicans, Fascists and Socialists. La Grande Italia presents a sweeping study of the development of Italian national identity in all its incarnations throughout the twentieth century. This important contribution to the study of modern Italian nationalism and the ambition to achieve a "great Italy" between the unification of Italy and the advent of the Italian Republic will appeal to anyone interested in modern European history, Fascism, and nationalism. Best Books for Special Interests, selected by the American Association of School Librarians, and Best Books for Regional General Interests, selected by the Public Library Association
Student, collaborator and lifelong friend of Enrico Fermi, Emilio Segrè presents a rich, well-rounded portrait of the scientist, his methods, intellectual history, and achievements. Explaining in nontechnical terms the scientific problems Fermi faced or solved, Enrico Fermi, Physicist contains illuminating material concerning Fermi's youth in Italy and the development of his scientific style. Emilio Segre was awarded the Nobel Prize for Physics in 1959.
The history of civilisations and places conveys the importance of the role the culture of sport and a cultivated management of leisure play in the definition of the identity of peoples and communities. Elevating such realms to the status of cultural assets to be shared and enhanced by analysing the dynamics of transformation of the city and territory related to them is a sensible, necessary and ethically correct action. The context of European architecture shows an increasing number of plans that both transform existing facilities and create new ones with a defining and strategic role in the development of urban and landscape fabrics. Activating a basic and permanent theoretical discussion is a fundamental and strategic action for the credibility and professional values of a sector that powerfully conveys the need to update and retrain its technical, executive and managerial personnel through a renewed cultural approach. The goal of this book is promoting awareness about the design enhancement of sport infrastructures as collective assets capable of developing identity and citizenship, through the analysis of both physical and immaterial factors and of the personnel charged with their conception, construction and management. Within contemporary architecture, the design of facilities for sport practice provides an extraordinary opportunity for the adaptation and strategic re-evaluation of the environment and its paradigmatic places. At the same time, sport infrastructures provide a crucial opportunity for architectural, design and technological experimentation – exploring their core features and enhance their potential is the main goal of this book.
Josâe Marâia, a young Spaniard studying at the Real Academia Espaänola in Rome during the Spanish Civil War, and his beloved Montse become involved with Junio, a pro-Nazi Italian prince, in a search for the map God used to create the Earth.
* Contains research and survey articles by well known and respected mathematicians on recent developments and research trends in differential geometry and topology * Dedicated in honor of Lieven Vanhecke, as a tribute to his many fruitful and inspiring contributions to these fields * Papers include all necessary introductory and contextual material to appeal to non-specialists, as well as researchers and differential geometers
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