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  2. Differential geometry - Wikipedia

    en.wikipedia.org/wiki/Differential_geometry

    Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds.It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra.

  3. List of unsolved problems in mathematics - Wikipedia

    en.wikipedia.org/wiki/List_of_unsolved_problems...

    Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.

  4. Ricci calculus - Wikipedia

    en.wikipedia.org/wiki/Ricci_calculus

    Jan Arnoldus Schouten developed the modern notation and formalism for this mathematical framework, and made contributions to the theory, during its applications to general relativity and differential geometry in the early twentieth century. [5] The basis of modern tensor analysis was developed by Bernhard Riemann in a paper from 1861. [6]

  5. Differentiable curve - Wikipedia

    en.wikipedia.org/wiki/Differentiable_curve

    The differential-geometric properties of a parametric curve (such as its length, its Frenet frame, and its generalized curvature) are invariant under reparametrization and therefore properties of the equivalence class itself. The equivalence classes are called C r-curves and are central objects studied in the differential geometry of curves.

  6. Differential geometry of surfaces - Wikipedia

    en.wikipedia.org/wiki/Differential_geometry_of...

    The differential geometry of surfaces revolves around the study of geodesics. It is still an open question whether every Riemannian metric on a 2-dimensional local chart arises from an embedding in 3-dimensional Euclidean space: the theory of geodesics has been used to show this is true in the important case when the components of the metric ...

  7. Mathematical analysis - Wikipedia

    en.wikipedia.org/wiki/Mathematical_analysis

    A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. [21] [22] [23] Differential equations play a prominent role in engineering, physics, economics, biology, and other disciplines.

  8. Geometric analysis - Wikipedia

    en.wikipedia.org/wiki/Geometric_analysis

    Geometric analysis is a mathematical discipline where tools from differential equations, especially elliptic partial differential equations (PDEs), are used to establish new results in differential geometry and differential topology. The use of linear elliptic PDEs dates at least as far back as Hodge theory.

  9. List of differential geometry topics - Wikipedia

    en.wikipedia.org/wiki/List_of_differential...

    Development (differential geometry) connection form; Cartan connection. affine connection; conformal connection; projective connection; method of moving frames;