Differential Geometry and Topology, Discrete and Computational Geometry

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Editors
Morvan, J.-M., Boucetta, M.
Pub. date
July 2005
Pages
388
Binding
hardcover
Volume
197 of NATO Science Series, III: Computer and Systems Sciences
ISBN print
978-1-58603-507-5
ISBN online
978-1-60750-113-8
Subject
Computer & Communication Sciences, Computer Science
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The aim of this volume is to give an introduction and overview to differential topology, differential geometry and computational geometry with an emphasis on some interconnections between these three domains of mathematics. The chapters give the background required to begin research in these fields or at their interfaces. They introduce new research domains and both old and new conjectures in these different subjects show some interaction between other sciences close to mathematics. Topics discussed are; the basis of differential topology and combinatorial topology, the link between differential geometry and topology, Riemanian geometry (Levi-Civita connextion, curvature tensor, geodesic, completeness and curvature tensor), characteristic classes (to associate every fibre bundle with isomorphic fiber bundles), the link between differential geometry and the geometry of non smooth objects, computational geometry and concrete applications such as structural geology and graphism.