Differential geometry

related topics
{math, number, function}
{math, energy, light}
{theory, work, human}
{rate, high, increase}

Differential geometry is a mathematical discipline using the techniques 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 Poincaré 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.


Full article ▸

related documents
Least squares
Mathematical constant
Dirac delta function
Shor's algorithm
Hausdorff dimension
Riemannian manifold
Exponential function
Metric space
Set (mathematics)
Semidirect product
Communication complexity
Taylor's theorem
Extended Euclidean algorithm
Template (programming)
Category theory
Cholesky decomposition
Square root
Vigenère cipher
Plane (geometry)
Icon (programming language)
Kernel (matrix)
Tail recursion
P = NP problem
Equivalence relation
Cantor's diagonal argument