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Variétés de contact. --- Contact manifolds --- Geometrie differentielle

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The aim of this book is to give an account of some important new developments in the study of the Yamabe problem on quaternionic contact manifolds. This book covers the conformally flat case of the quaternionic Heisenberg group or sphere, where complete and detailed proofs are given, together with a chapter on the conformal curvature tensor introduced very recently by the authors. The starting point of the considered problems is the well-known Folland-Stein Sobolev type embedding and its sharp form that is determined based on geometric analysis. This book also sits at the interface of the gene

Geometry, Differential. --- Contact manifolds. --- Group theory.

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Contact manifolds. --- Submanifolds. --- Geometry. --- Geometry, Differential --- Manifolds (Mathematics) --- Manifolds, Contact --- Almost contact manifolds --- Differentiable manifolds --- Mathematics --- Euclid's Elements --- Subvarietats (Matemàtica) --- Geometria diferencial --- Varietats (Matemàtica)

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This textbook offers a concise introduction to symplectic and contact geometry, with a focus on the relationships between these subjects and other topics such as Lie theory and classical mechanics. Organized into four chapters, this work serves as a stepping stone for readers to delve into the subject, providing a succinct and motivating foundation. The content covers definitions, symplectic linear algebra, symplectic and contact manifolds, Hamiltonian systems, and more. Prerequisite knowledge includes differential geometry, manifolds, algebraic topology, de Rham cohomology, and the basics of Lie groups. Quick reviews are included where necessary, and examples and constructions are provided to foster understanding. Ideal for advanced undergraduate students and graduate students, this volume can also serve as a valuable resource for independent researchers seeking a quick yet solid understanding of symplectic and contact geometry.

Geometry, Differential. --- Manifolds (Mathematics). --- Differential Geometry. --- Manifolds and Cell Complexes. --- Contact manifolds. --- Symplectic geometry.

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Geometry, Differential --- Symplectic geometry --- Contact manifolds --- Géométrie différentielle. --- Géométrie symplectique. --- Variétés de contact. --- Géométrie différentielle. --- Géométrie symplectique. --- Variétés de contact.