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On the geometry of affine Kähler immersions
Published online by Cambridge University Press: 22 January 2016
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In this paper we extend the work on affine immersions [N-Pi]-1 to the case of affine immersions between complex manifolds and lay the foundation for the geometry of affine Kähler immersions. The notion of affine Kähler immersion extends that of a holomorphic and isometric immersion between Kähler manifolds and can be contrasted to the notion of holomorphic affine immersion which has been established in the work of Dillen, Vrancken and Verstraelen [D-V-V] and that of Abe [A].
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- Copyright © Editorial Board of Nagoya Mathematical Journal 1990
References
[D-V-V]
Dillen, F., Vrancken, L. and Verstraelen, L., Complex affine differential geometry, Atti. Accad. Peloritana Pericolanti CI. Sci. Fis. Mat. Nat. LXVI (1988), 231–260.Google Scholar
[K-N]
Kobayashi, S. and Nomizu, K., Foundations of Differential Geometry, vol I, II
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[N-Pi]-1
Nomizu, K. and Pinkall, U., On the geometry of affine immersions, Math. Z., 195 (1987), 165–178.CrossRefGoogle Scholar
[N-Pi]-2
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[N-Po]
Nomizu, K. and Podestà, F.
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[N-S]
Nomizu, K. and Smyth, B., Differential geometry for complex hypersurfaces II, J. Math. Soc. Japan, 20 (1968), 498–521.Google Scholar
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