Bochner identity

From Wikipedia
https://en.wikipedia.org/wiki/Bochner_identity

In mathematics — specifically, differential geometry — the Bochner identity is an identity concerning harmonic maps between Riemannian manifolds. The identity is named after the American mathematician Salomon Bochner.

Statement of the result

Let M and N be Riemannian manifolds and let u : M → N be a harmonic map. Let du denote the derivative (pushforward) of u, ∇ the gradient, Δ the Laplace–Beltrami operator, RiemN the Riemann curvature tensor on N and RicM the Ricci curvature tensor on M. Then

See also

References

  • Eells, J; Lemaire, L. (1978). "A report on harmonic maps". Bull. London Math. Soc. 10 (1): 1–68. doi: 10.1112/blms/10.1.1. MR  0495450.

External links