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 Shigeo 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., vol. 1198, Berlin, New York: Springer-Verlag, pp. 88–97, doi:10.1007/BFb0077045, ISBN 978-3-540-16762-4, MR 0874763 Demailly, Jean-Pierre (2012), Complex Analytic and Differential Geometry (PDF) 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 (12): 1268–1273, Bibcode:1953PNAS...39.1268K, doi:10.1073/pnas.39.12.1268, ISSN 0027-8424, JSTOR 89226, MR 0066693, PMC 1063947, PMID 16589409