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Projective and affine transformations of a complex symmetric connection

Published online by Cambridge University Press:  17 April 2009

Novica Blažić  and
Neda Bokan
Novica Blažić
Affiliation:
Faculty of Mathematics University of BelgradeStudentski trg 16, p.p. 550 11000 BelgradeYugoslavia e-mail: epmfm07%yubgss21%fon.uucp@moumee.calstatela.edu.epmfm06%yubgss21%fon.uucp@moumee.calstatela.edu.
Neda Bokan
Affiliation:
Faculty of Mathematics University of BelgradeStudentski trg 16, p.p. 550 11000 BelgradeYugoslavia e-mail: epmfm07%yubgss21%fon.uucp@moumee.calstatela.edu.epmfm06%yubgss21%fon.uucp@moumee.calstatela.edu.
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Abstract

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Let M be a compact complex manifold and ∇ an arbitrary complex (not necessarily Riemannian) connection. In this paper we study the relation between the geometry of (M, ∇) and the topology of M, that is, we are interested in the following problem: To what extent does the topology of M determine the relations between the group of holomorphically projective transformations, the group of projective transformations and the group of affine transformations on M? Under assumptions on the Ricci-type tensors of ∇ and Chern numbers of M we show that a holomorphically projective transformation and a projective transformation are in fact affine transformations on M. A family of interesting examples of connections of this kind are constructed. Also, the case when M is a Kähler manifold is studied.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 50 , Issue 2 , October 1994 , pp. 337 - 347
Copyright
Copyright © Australian Mathematical Society 1994

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