Bochner–Kodaira–Nakano identity

In mathematics, the Bochner–Kodaira–Nakano identity is an analogue of the Weitzenböck identity for hermitian manifolds, giving an expression for the antiholomorphic Laplacian of a vector bundle over a hermitian manifold in terms of its complex conjugate and the curvature of the bundle and the torsion of the metric of the manifold. It is named after Salomon Bochner, Kunihiko Kodaira, and Hidegorô Nakano.

References

• Demailly, Jean-Pierre (1986), "Sur l'identité de Bochner-Kodaira-Nakano en géométrie hermitienne", Séminaire d'analyse P. Lelong-P. Dolbeault-H. Skoda, années 1983/1984, Lecture Notes in Math. 1198, Berlin, New York: Springer-Verlag, pp. 88–97, doi:10.1007/BFb0077045, MR 874763 
• Demailly, Jean-Pierre (2012), Complex Analytic and Differential Geometry 
• Kodaira, Kunihiko (1953), "On a differential-geometric method in the theory of analytic stacks", Proceedings of the National Academy of Sciences of the United States of America 39: 1268–1273, doi:10.1073/pnas.39.12.1268, ISSN 0027-8424, MR 0066693