Ricci curvature

2-tensor obtained as a contraction of the Riemann curvature 4-tensor on a Riemannian manifold (or, more generally, a smooth manifold equipped with affine connection)
Thing tensor_field Q1195879
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Ricci curvature

Summary

Ricci curvature is a tensor field[1]. It draws 295 Wikipedia views per month (tensor_field category, ranking #1 of 2).[2]

Key Facts

  • Ricci curvature is credited with the discovery of Gregorio Ricci-Curbastro[3].
  • Ricci curvature's image is recorded as Penrose ricci tensor.svg[4].
  • Ricci curvature's instance of is recorded as tensor field[5].
  • Gregorio Ricci-Curbastro is named after Ricci curvature[6].
  • Ricci curvature's time of discovery or invention is recorded as +1900-00-00T00:00:00Z[7].
  • Ricci curvature's Freebase ID is recorded as /m/01pdpm[8].
  • Ricci curvature's defining formula is recorded as \operatorname{Ric}(X,Y)= \operatorname{tr}(\operatorname{Riem}(X,-)Y)[9].
  • Ricci curvature's MathWorld ID is recorded as RicciCurvatureTensor[10].
  • Ricci curvature's nLab ID is recorded as Ricci curvature[11].
  • Ricci curvature's schematic is recorded as RicciTensor.svg[12].
  • Ricci curvature's maintained by WikiProject is recorded as WikiProject Mathematics[13].
  • Ricci curvature's Microsoft Academic ID is recorded as 12089564[14].
  • Ricci curvature's in defining formula is recorded as \operatorname{Ric}[15].
  • Ricci curvature's in defining formula is recorded as \operatorname{Riem}[16].
  • Ricci curvature's Encyclopedia of Mathematics article ID is recorded as Ricci_tensor[17].
  • Ricci curvature's PlanetMath ID is recorded as RicciTensor[18].
  • Ricci curvature's Namuwiki ID is recorded as 리치 텐서[19].
  • Ricci curvature's Treccani's Enciclopedia della Matematica ID is recorded as tensore-di-ricci[20].
  • Ricci curvature's Enciclopedia della Scienza e della Tecnica ID is recorded as tensore-di-ricci[21].
  • Ricci curvature's OpenAlex ID is recorded as C12089564[22].
  • Ricci curvature's ScienceDirect topic ID is recorded as mathematics/ricci-tensor[23].

Body

Works and Contributions

Ricci curvature is credited with the discovery of Gregorio Ricci-Curbastro[3].

Why It Matters

Ricci curvature draws 295 Wikipedia views per month (tensor_field category, ranking #1 of 2).[2] It has Wikipedia articles in 16 language editions, a strong signal of global cultural recognition.[24] It is known by 26 alternative names across languages and contexts.[25]

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [4] . wikidata.org.
  2. [5] . wikidata.org.
  3. [3] . wikidata.org.
  4. [6] . wikidata.org.
  5. [7] . wikidata.org.
  6. [8] . Freebase Data Dumps. wikidata.org.
  7. [9] . wikidata.org.
  8. [10] . wikidata.org.
  9. [11] . wikidata.org.
  10. [12] . wikidata.org.
  11. [13] . wikidata.org.
  12. [14] . wikidata.org.
  13. [15] . wikidata.org.
  14. [16] . wikidata.org.
  15. [17] . wikidata.org.
  16. [18] . wikidata.org.
  17. [19] . wikidata.org.
  18. [20] . wikidata.org.
  19. [21] . wikidata.org.
  20. [22] . OpenAlex. Retrieved . docs.openalex.org. Provenance: wikidata.org.
  21. [23] . wikidata.org.

Class ancestry

  1. [1] . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] . Wikimedia Foundation. dumps.wikimedia.org.
  2. [24] . Wikidata sitelinks. wikidata.org.
  3. [25] . Wikidata aliases. wikidata.org.

📑 Cite this page

Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). Ricci curvature. Retrieved May 3, 2026, from https://4ort.xyz/entity/ricci-curvature
MLA “Ricci curvature.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 2026, https://4ort.xyz/entity/ricci-curvature.
BibTeX @misc{4ortxyz_ricci-curvature_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{Ricci curvature}}, year = {2026}, url = {https://4ort.xyz/entity/ricci-curvature}, note = {Accessed: 2026-05-03}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): Ricci curvature — https://4ort.xyz/entity/ricci-curvature (retrieved 2026-05-03)

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