Celebratio Mathematica

R. Bott and S. S. Chern: “Hermitian vector bundles and the equidistribution of the zeroes of their holomorphic sections,” Acta Math. 114 : 1 (1965), pp. 71–112. A Russian translation was published in Matematika 14:2 (1970). MR 0185607 Zbl 0148.31906 article

R. Bott and S. S. Chern: “Some formulas related to complex transgression,” pp. 48–57 in Essays on topology and related topics: Mémoires dédiés à Georges de Rham [Essays on topology and related topics: Memoirs dedicated to Georges de Rham]. Edited by A. Haefliger and R. Narasimhan. Springer (New York), 1970. MR 0264715 Zbl 0203.54202 incollection

Let \( X \) be a complex manifold of complex dimension \( n \) and \( \pi:E\to X \) a holomorphic vector bundle whose fiber dimension is also \( n \). On \( E \) we introduce a positive definite hermitian norm \( N \) and denote by \[ B^*(E) = \{e\in E\mid 0 < N(e)\} \] the subset of non-zero vectors of \( E \). Let \( c_n(E) \) be the Chern form of the hermitian structure (to be described again below). In [1965] we proved the theorem: There exists a real-valued form \( \rho \) of type \( (n-1, \) \( n-1) \) on \( B^*(E) \) such that \begin{equation*}\tag{1} \pi^* c_n(E) = \frac{dd^c}{4\pi}\rho. \end{equation*} In this paper we wish to give a proof of (1) based on an explicit construction. We will follow and extend a formalism developed in the real case by H. Flanders [1953]. It is possible that this formalism will be useful for later purposes.

Georges de Rham	Related
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R. Bott: “For the Chern volume,” pp. 106–108 in S. S. Chern: A great geometer of the twentieth century (Los Angeles, 1990). Edited by S.-T. Yau. International Press (Cambridge, MA), 1992. MR 1201350 incollection

Raoul H. Bott	Related	Volume
Shing-Tung Yau	Related

misc J. Simons, R. Bott, R. Bryant, X.-X. Chen, S.-S. Chern, F. Hirzebruch, B. Lawson, K. Liu, E. Meinrenken, C.-L. Terng, and A. Weinstein: The Chern Symposium, 1998. Selections from MSRI’s Video Archive no. 2 (CD-ROM), recorded Berkelely, CA, 5–7 March 1998. MR 1731157 Zbl 1079.00505

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H. Blaine Lawson, Jr.	Related
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Kefeng Liu	Related
Ekhard Meinrenken	Related

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