Bochner–Kodaira–Nakano identity: Difference between revisions
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Adding short description: "Expression for the antiholomorphic Laplacian of a vector bundle over a hermitian manifold" (Shortdesc helper) |
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*{{Citation | author1-link=Jean-Pierre Demailly | last1=Demailly | first1=Jean-Pierre | title=Séminaire d'analyse P. Lelong-P. Dolbeault-H. Skoda, années 1983/1984 | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=Lecture Notes in Math. | doi=10.1007/BFb0077045 |mr=874763 | year=1986 | volume=1198 | chapter=Sur l'identité de Bochner-Kodaira-Nakano en géométrie hermitienne | pages=88–97| isbn=978-3-540-16762-4 }} |
*{{Citation | author1-link=Jean-Pierre Demailly | last1=Demailly | first1=Jean-Pierre | title=Séminaire d'analyse P. Lelong-P. Dolbeault-H. Skoda, années 1983/1984 | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=Lecture Notes in Math. | doi=10.1007/BFb0077045 |mr=874763 | year=1986 | volume=1198 | chapter=Sur l'identité de Bochner-Kodaira-Nakano en géométrie hermitienne | pages=88–97| isbn=978-3-540-16762-4 }} |
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*{{Citation | author1-link=Jean-Pierre Demailly | last1=Demailly | first1=Jean-Pierre | title= Complex Analytic and Differential Geometry | url=http://www-fourier.ujf-grenoble.fr/~demailly/manuscripts/agbook.pdf | year=2012}} |
*{{Citation | author1-link=Jean-Pierre Demailly | last1=Demailly | first1=Jean-Pierre | title= Complex Analytic and Differential Geometry | url=http://www-fourier.ujf-grenoble.fr/~demailly/manuscripts/agbook.pdf | year=2012}} |
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*{{Citation | last1=Kodaira | first1=Kunihiko | authorlink = Kunihiko Kodaira | title=On a differential-geometric method in the theory of analytic stacks |mr=0066693 | year=1953 | journal=[[Proceedings of the National Academy of Sciences|Proceedings of the National Academy of Sciences of the United States of America]] | issn=0027-8424 | volume=39 | issue=12 | pages=1268–1273 | doi=10.1073/pnas.39.12.1268 | pmid=16589409 | jstor=89226 | pmc=1063947}} |
*{{Citation | last1=Kodaira | first1=Kunihiko | authorlink = Kunihiko Kodaira | title=On a differential-geometric method in the theory of analytic stacks |mr=0066693 | year=1953 | journal=[[Proceedings of the National Academy of Sciences|Proceedings of the National Academy of Sciences of the United States of America]] | issn=0027-8424 | volume=39 | issue=12 | pages=1268–1273 | doi=10.1073/pnas.39.12.1268 | pmid=16589409 | jstor=89226 | pmc=1063947| bibcode=1953PNAS...39.1268K | doi-access=free }} |
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Latest revision as of 06:25, 22 August 2021
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
[edit]- 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
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