# Bochner identity

*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 d*u* denote the derivative (pushforward) of *u*, ∇ the
gradient, Δ the
Laplace–Beltrami operator, Riem_{N} the
Riemann curvature tensor on *N* and Ric_{M} 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