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Affine Maps, Euclidean Motions and Quadrics
Affine geometry and quadrics are fascinating subjects alone, but they are also important applications of linear algebra. They give a first glimpse into the world of algebraic geometry yet they are equally relevant to a wide range of disciplines such as engineering. This text discusses and classifies affinities and Euclidean motions culminating in classification results for quadrics. A high level of detail and generality is a key feature unmatched by other books available. Such intricacy makes this a particularly accessible teaching resource as it requires no extra time in deconstructing the author’s reasoning. The provision of a large number of exercises with hints will help students to de...
Geometria axiomàtica
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Differential Geometry
This volume contains research and expository papers on recent advances in foliations and Riemannian geometry. Some of the topics covered in this volume include: topology, geometry, dynamics and analysis of foliations, curvature, submanifold theory, Lie groups and harmonic maps.Among the contributions, readers may find an extensive survey on characteristic classes of Riemannian foliations offering also new results, an article showing the uniform simplicity of certain diffeomorphism groups, an exposition of convergences of contact structures to foliations from the point of view of Thurston's and Thurston?Bennequin's inequalities, a discussion about Fatou?Julia decompositions for foliations and...
Geometria projectiva
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Afinitats, moviments i quàdriques
En aquest llibre es dóna un model algebraic, sustentat en el concepte d’espai vectorial, on, amb definicions adequades, es compleixen tots els axiomes de la geometria afí i euclidiana clàssica. D’aquest objecte algebraic se’n diu espai afí. S’estudien i es classifiquen les aplicacions naturals entre aquests espais: les afinitats. S’introdueix el concepte de distància i s’estudien i es classifiquen les afinitats que conserven la distància: els moviments. Finalment, s’estudien i es classifiquen les figures més elementals d’aquests espais, a part dels punts i les rectes: les quàdriques. Agustí Reventós Tarrida és professor del Departament de Matemà-tiques de la Unive...
