Articles on Differential Geometry, Including - Sphere, Symplectic Manifold, Tangent Space, Tangent, Pseudosphere, Curvature, Shape of the Universe, Gauss "Bonnet Theorem, Diffeology, Calabi "Yau Manifold, Metric Tensor (Paperback)

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Hephaestus Books represents a new publishing paradigm, allowing disparate content sources to be curated into cohesive, relevant, and informative books. To date, this content has been curated from Wikipedia articles and images under Creative Commons licensing, although as Hephaestus Books continues to increase in scope and dimension, more licensed and public domain content is being added. We believe books such as this represent a new and exciting lexicon in the sharing of human knowledge. This particular book is a collaboration focused on Differential geometry.More info: Differential geometry is a mathematical discipline that uses the methods of differential and integral calculus, as well as linear and multilinear algebra, to study problems in geometry. The theory of plane and space curves and of surfaces in the three-dimensional Euclidean space formed the basis for its initial development in the eighteenth and nineteenth century. Since the late nineteenth century, differential geometry has grown into a field concerned more generally with geometric structures on differentiable manifolds. It is closely related to differential topology, and to the geometric aspects of the theory of differential equations. Grigori Perelman's proof of the Poincar conjecture using the techniques of Ricci flow demonstrated the power of the differential-geometric approach to questions in topology and highlighted the important role played by the analytic methods. Differential geometry of surfaces already captures many of the key ideas and techniques characteristic of the field.