Concepedia

Affine Connections

Affine Connection is a geometric structure on a smooth manifold that assigns to each pair of vector fields a new vector field, specifying a rule for parallel transport of vectors along curves in a manner consistent with affine transformations, thereby enabling the differentiation of vector fields in the absence of a metric.

283

Publications

10.3K

Citations

342

Authors

239

Institutions

Publications per year

2017–2026

30

Variants

Affine Connection

Parents

Publications

283

Invariant Affine Connections on Homogeneous Spaces

Katsumi Nomizu · American Journal of Mathematics · 1954 · 533 citations · Full text

, , +14

Differential Geometry of Curved Exponential Families-Curvatures and Information Loss

The Annals of Statistics · 1982 · 376 citations · Full text

, , +13

Differential geometry on the space of connections via graphs and projective limits

Abhay Ashtekar, Jerzy Lewandowski · Journal of Geometry and Physics · 1995 · 302 citations · Full text

, , +12

Fundamental solutions and geometry of the sum of squares of vector fields

Antonio S�nchez-Calle · Inventiones mathematicae · 1984 · 217 citations

, , +13

Information geometry of Boltzmann machines

K. Kurata, Hiroshi Nagaoka · IEEE Transactions on Neural Networks · 1992 · 199 citations

, , +11

1–5 of 283

Authors

342

  1. BO
    Barbara Opozda

    Jagiellonian University, Poland

    8 publications · 191 citations

    8

    h-index

  2. MS
    Mića S. Stanković

    University of Nis, Serbia

    7 publications · 108 citations

    7

    h-index

  3. KN
    Katsumi Nomizu

    Brown University, United States

    7 publications · 731 citations

    7

    h-index

  4. JM
    Josef Mikeš

    Palacký University Olomouc, Czechia

    6 publications · 124 citations

    6

    h-index

  5. MO
    Morio Obata

    Tokyo Metropolitan University, Japan

    5 publications · 204 citations

    5

    h-index

1–5 of 342

Institutions

239

  1. Jagiellonian University

    Krakow, Poland

    7 h-index

    7 publications

    178 citations

  2. University of Nis

    Niš, Serbia

    6 h-index

    12 publications

    202 citations

  3. Tokyo Metropolitan University

    Tokyo, Japan

    6 h-index

    7 publications

    293 citations

  4. Palacký University Olomouc

    Olomouc, Czechia

    6 h-index

    7 publications

    96 citations

  5. Institute of Mathematics

    Warsaw, Poland

    6 h-index

    7 publications

    158 citations

  6. Charles University

    Prague, Czechia

    5 h-index

    9 publications

    231 citations

  7. University of Warsaw

    Warsaw, Poland

    5 h-index

    5 publications

    368 citations

  8. Centre National de la Recherche Scientifique

    Paris, France

    5 h-index

    8 publications

    156 citations

1–8 of 239

Venues

  1. Nagoya Mathematical Journal

    12 publications · 451 citations

    12

    h-index

  2. Journal of Mathematical Physics

    10 publications · 204 citations

    10

    h-index

  3. Classical and Quantum Gravity

    9 publications · 215 citations

    9

    h-index

  4. Transactions of the American Mathematical Society

    TRAN · 8 publications · 417 citations

    8

    h-index

  5. Journal of Differential Geometry

    7 publications · 259 citations

    7

    h-index

1–5