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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 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


bochner, kodaira, nakano, identity, mathematics, analogue, weitzenböck, identity, hermitian, manifolds, giving, expression, antiholomorphic, laplacian, vector, bundle, over, hermitian, manifold, terms, complex, conjugate, curvature, bundle, torsion, metric, ma. In mathematics the Bochner Kodaira Nakano identity is an analogue of the Weitzenbock 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 EditDemailly Jean Pierre 1986 Sur l identite de Bochner Kodaira Nakano en geometrie hermitienne Seminaire d analyse P Lelong P Dolbeault H Skoda annees 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 This differential geometry related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Bochner Kodaira Nakano identity amp oldid 1040023337, wikipedia, wiki, book, books, library,

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