Concepedia

Curvature Operator

The **Curvature Operator** is a symmetric linear operator on the space of bivectors that encodes the Riemann curvature tensor by mapping each pair of tangent vectors to their sectional curvature contribution, thereby characterizing the intrinsic geometric deformation of a Riemannian manifold.

408

Publications

23.4K

Citations

557

Authors

301

Institutions

Publications per year

2017–2026

53

Parents

Publications

408

The Self-Duality Equations on a Riemann Surface

Nigel Hitchin · Proceedings of the London Mathematical Society · 1987 · 1.8K citations

, , +13

A Riemannian Framework for Tensor Computing

Xavier Pennec, Pierre Fillard, Nicholas Ayache · International Journal of Computer Vision · 2005 · 1.6K citations · Full text

, , +14

Four-manifolds with positive curvature operator

Richard S. Hamilton · Journal of Differential Geometry · 1986 · 808 citations · Full text

, , +15

The geometry of tensor calculus, I

André Joyal, Ross Street · Advances in Mathematics · 1991 · 671 citations

, , +12

On the evolution of harmonic mappings of Riemannian surfaces

Michaël Struwe · Commentarii Mathematici Helvetici · 1985 · 502 citations

, , +11

1–5 of 408

Authors

557

  1. EG
    Erhan Güler

    Bartin University, Türkiye

    8 publications · 141 citations

    8

    h-index

  2. PG
    Peter Gilkey

    University of Oregon, United States

    7 publications · 131 citations

    7

    h-index

  3. EG
    Eduardo García‐Río

    Universidade de Santiago de Compostela, Spain

    6 publications · 105 citations

    6

    h-index

  4. YL
    Yanlin Li

    Hangzhou Normal University, China

    6 publications · 104 citations

    6

    h-index

  5. AG
    Alfred Gray

    University of California, Santa Barbara, United States

    5 publications · 358 citations

    5

    h-index

1–5 of 557

Institutions

301

  1. Rutgers, The State University of New Jersey

    New Brunswick, United States

    7 h-index

    9 publications

    482 citations

  2. Universidade de Santiago de Compostela

    Santiago de Compostela, Spain

    7 h-index

    15 publications

    275 citations

  3. Bartin University

    Bartın, Türkiye

    7 h-index

    9 publications

    189 citations

  4. Tsinghua University

    Beijing, China

    6 h-index

    12 publications

    465 citations

  5. West University of Timişoara

    Timișoara, Romania

    6 h-index

    8 publications

    268 citations

  6. Princeton University

    Princeton, United States

    6 h-index

    7 publications

    233 citations

  7. UCLouvain

    Louvain-la-Neuve, Belgium

    6 h-index

    6 publications

    214 citations

  8. Hangzhou Normal University

    Hangzhou, China

    6 h-index

    8 publications

    138 citations

1–8 of 301

Venues

  1. Journal of Differential Geometry

    12 publications · 1.5K citations

    12

    h-index

  2. Proceedings of the American Mathematical Society

    PROC · 13 publications · 430 citations

    11

    h-index

  3. Pacific Journal of Mathematics

    10 publications · 255 citations

    10

    h-index

  4. arXiv (Cornell University)

    Repository · 10 publications · 190 citations

    10

    h-index

  5. Classical and Quantum Gravity

    9 publications · 369 citations

    9

    h-index

1–5