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Differential geometry Home About Me Archives Sitemap Lorem Ipsum Differential geometry is a mathematical discipline that uses the methods of differential and integral calculus 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 with differential topology and with the geometric aspects of the theory of differential equations . The proof of the Poincare 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. Contents Branches of differential geometry Riemannian geometry Pseudo-Riemannian geometry Finsler geometry ... External links Branches of differential geometry Riemannian geometry Main article: Riemannian geometry Riemannian geometry studies Riemannian manifolds smooth manifolds with a Riemannian metric , a notion of a distance expressed by means of a positive definite symmetric bilinear form defined on the tangent space at each point. Riemannian geometry generalizes

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Differential geometry Jump to: navigation search Differential geometry is a mathematical discipline that uses the methods of differential and integral calculus 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 with differential topology and with the geometric aspects of the theory of differential equations . The proof of the Poincare 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. Branches of differential geometry Riemannian geometry Pseudo-Riemannian geometry Finsler geometry ... External links Main article: Riemannian geometry Riemannian geometry studies Riemannian manifolds smooth manifolds with a Riemannian metric , a notion of a distance expressed by means of a positive definite symmetric bilinear form defined on the tangent space at each point. Riemannian geometry generalizes

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