Celebratio Mathematica — Chern

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Works connected to Donald Clayton Spencer

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incollection S.-S. Chern: “On a generalization of Kähler geometry,” pp. 103–121 in Algebraic geometry and topology: A symposium in honor of S. Lefschetz (Princeton, NJ, 8–10 April 1954). Edited by R. H. Fox, D. C. Spencer, and A. W. Tucker. Princeton Mathematical Series 12. Princeton University Press, 1957. MR 0087172 Zbl 0078.14103

Ralph Hartzler Fox	Related
Solomon Lefschetz	Related
Albert William Tucker	Related
Donald Clayton Spencer	Related

incollection S. S. Chern, H. I. Levine, and L. Nirenberg: “Intrinsic norms on a complex manifold,” pp. 119–139 in Global analysis: Papers in Honor of K. Kodaira. Edited by D. C. Spencer. University Tokyo Press, 1969. MR 0254877 Zbl 0202.11603

We propose to define in this paper certain norms (or more precisely, semi-norms) on the homology groups of a complex manifold. They will be invariants of the complex strucgture and do not increase under holomorphic mappings. Their definitions depend on the bounded plurisubharmonic functions on the manifold and are modelled after the notion of harmonic length introduced by H. Landau and R. Osserman [1959–1960] for Riemann surfaces (= one-dimensional complex manifolds). It is possible to extend the definition to certain families of chains. In particular we get in this way an intrinsic pseudo-metric on the manifold which is closely related to that of Carathéodory [1927] and to one recently introduced by S. Kobayashi [1967].

Kunihiko Kodaira	Related
Harold I. Levine	Related
Louis Nirenberg	Related
Donald Clayton Spencer	Related

book Collection of articles dedicated to S. S. Chern and D. C. Spencer on their sixtieth birthdays, published as J. Diff. Geom. 6 : 4. Lehigh University (Bethlehem, PA), 1972. MR 0317858