Einstein manifolds

Besse, A. L. (1987). Einstein manifolds. Springer-Verlag.

Type

Book chapter

Intellectual base

Review or monograph

Year

1987

DOI

10.1007/978-3-540-74311-8

Link

https://doi.org/10.1007/978-3-540-74311-8

Cited by

3 citations across 3 artifacts.

Domain-specific

• Einstein manifold
  • For dimension greater than two the proportionality factor is constant on each connected component under standard hypotheses; the condition includes constant-curvature spaces but permits richer Weyl curvature.
• Quaternion-Kähler Manifold
  • In dimension four, authors use a separate convention tied to oriented self-dual Einstein geometry; the holonomy condition alone is then vacuous and must not be used as the recognition test.
• Riemannian manifold
  • Positive definiteness distinguishes Riemannian from pseudo-Riemannian geometry, the metric is extra structure rather than intrinsic to a smooth manifold and coordinate coefficients transform tensorially.

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