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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The Schwarzian derivative for maps between manifolds with complex projective connections


Authors: Robert Molzon and Karen Pinney Mortensen
Journal: Trans. Amer. Math. Soc. 348 (1996), 3015-3036
MSC (1991): Primary 53B10, 32H02
MathSciNet review: 1348154
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Abstract: In this paper we define, in two equivalent ways, the Schwarzian derivative of a map between complex manifolds equipped with complex projective connections. Also, a new, coordinate-free definition of complex projective connections is given. We show how the Schwarzian derivative is related to the projective structure of the manifolds, to projective linear transformations, and to complex geodesics.


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Additional Information

Robert Molzon
Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506-0027
Email: molzon@ms.uky.edu

Karen Pinney Mortensen
Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506-0027
Email: pinney@ms.uky.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-96-01590-5
PII: S 0002-9947(96)01590-5
Received by editor(s): August 15, 1994
Additional Notes: The second author was partially supported by NSF grant DMS-9102976.
Article copyright: © Copyright 1996 American Mathematical Society