Abstract
In a previous paper ([9]) the author considered transmission problems for holomorphic fiber bundles over Riemann surfaces and families of Riemann surfaces. In this context the question arose as to how to treat analogous problems for fiber bundles over complex spaces X. The situation in higher dimensional complex spaces is by necessity different from the one dimensional case since only in more than one complex dimension the phenomenon of pseudoconvexity appears. At the same time it turned out to be desirable to deal with a more general geometric and analytic situation as in [9], thus making it possible to interpret “topologically correct” transmission problems as cycles in a certain homology theory, so that two such topological transmission problems are isomorphic if the corresponding cycles are homologous.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This research was supported by the Air Force Office of Scientific Research.
Received June 15, 1964.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bourbaki, N.: Topologie générale. Actualités Sci. Ind. 1142 (Paris) 1951.
Cartan, H.: Espaces fibres analytiques. Intern. Symp.alg.top., Univ. Nac. Mexico (1958), 97–121.
Giesecke, B.: Simpliziale Zerlegung abzählbarer analytischer Räume. Math. Zschr. 83, 177–213 (1964).
Grattert, H., und R. Remmert: Komplexe Räume. Math. Ann. 136, 245–318 (1958).
Hilton, P. J., and S. Wylie: Homology theory. Cambridge Univ. Press 1960.
Kerner, H.: Über die Automorphismengruppe kompakter komplexer Räume. Arch. Math. 11, 282–288 (1960).
Kneser, H.: Die Randwerte einer analytischen Funktion zweier Veränderlichen. Mh. Math. Phys. 43, 364–380 (1936).
Lewy, H.: On the local character of the solutions of an atypical linear partial differential equation . Ann. Math. 64, 514–522 (1956).
Röhrl, H.: Über das Riemann-Privalovsche Randwertproblem. Math. Ann. 151, 365–423 (1963).
Röhrl, H.: .Q-degenerate singular integral equations and holomorphic affine bundles over compact Riemann surfaces, II. (to appear).
Sommer, F.: Komplex-analytische Blätterung reeller Mannigfaltigkeiten im C. Math. Ann. 136, 111–133 (1958).
Whitney, H.: Geometrie integration theory. Princeton Univ. Press 1957.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1965 Springer-Verlag Berlin · Heidelberg
About this paper
Cite this paper
Röhrl, H. (1965). Transmission Problems for Holomorphic Fiber Bundles. In: Aeppli, A., Calabi, E., Röhrl, H. (eds) Proceedings of the Conference on Complex Analysis. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-48016-4_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-48016-4_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-48018-8
Online ISBN: 978-3-642-48016-4
eBook Packages: Springer Book Archive