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  2. Foundations of Differential Geometry - Wikipedia

    en.wikipedia.org/wiki/Foundations_of...

    Foundations of Differential Geometry is an influential 2-volume mathematics book on differential geometry written by Shoshichi Kobayashi and Katsumi Nomizu. The first volume was published in 1963 and the second in 1969, by Interscience Publishers. Both were published again in 1996 as Wiley Classics Library.

  3. Shoshichi Kobayashi - Wikipedia

    en.wikipedia.org/wiki/Shoshichi_Kobayashi

    The two-volume book Foundations of Differential Geometry, which he coauthored with Katsumi Nomizu, has been known for its wide influence. In 1970 he was an invited speaker for the section on geometry and topology at the International Congress of Mathematicians in Nice.

  4. List of differential geometry topics - Wikipedia

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

    Toggle Differential geometry of curves and surfaces subsection. ... Toggle Foundations subsection. 2.1 Calculus on manifolds. 2.2 Differential ... Download as PDF ...

  5. 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.

  6. Differential geometry - Wikipedia

    en.wikipedia.org/wiki/Differential_geometry

    Differential geometry finds applications throughout mathematics and the natural sciences. Most prominently the language of differential geometry was used by Albert Einstein in his theory of general relativity, and subsequently by physicists in the development of quantum field theory and the standard model of particle physics.

  7. Bochner's theorem (Riemannian geometry) - Wikipedia

    en.wikipedia.org/wiki/Bochner's_theorem...

    Foundations of differential geometry. Vol I. Interscience Tracts in Pure and Applied Mathematics. Vol. 15. Reprinted in 1996. New York–London: John Wiley & Sons, Inc. ISBN 0-471-15733-3. MR 0152974. Zbl 0119.37502. Kobayashi, Shoshichi (1972). "Isometries of Riemannian Manifolds". Transformation groups in differential geometry (PDF ...

  8. Curvature form - Wikipedia

    en.wikipedia.org/wiki/Curvature_form

    Let G be a Lie group with Lie algebra, and P → B be a principal G-bundle.Let ω be an Ehresmann connection on P (which is a -valued one-form on P).. Then the curvature form is the -valued 2-form on P defined by

  9. Ehresmann connection - Wikipedia

    en.wikipedia.org/wiki/Ehresmann_connection

    A covariant derivative in differential geometry is a linear differential operator which takes the directional derivative of a section of a vector bundle in a covariant manner. It also allows one to formulate a notion of a parallel section of a bundle in the direction of a vector: a section s is parallel along a vector X {\displaystyle X} if ∇ ...