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On the Cartan-Norden theorem for affine Kähler immersions

Published online by Cambridge University Press:  22 January 2016

Katsumi Nomizu  and
Fabio Podestà
Katsumi Nomizu
Affiliation:
Department of Mathematics, Brown University, Providence, RI 02912, U.S.A.
Fabio Podestà
Affiliation:
Fabio Podestà c/o Scoula Normale Superiore, Piazza Cavalieri 7, 1-56100 Pisa, Italy
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In [N-Pi-Po] the notion of affine Kähler immersion for complex manifolds has been introduced: if Mn is an n-dimensional complex manifold and f: Mn -→ Cn+1 is a holomorphic immersion together with an anti-holomorphic transversal vector field ζ, we can induce a connection ▽ on Mn which is Kähler-like, that is, its curvature tensor R satisfies R(Z, W) = 0 as long as Z, W are (1, 0) complex vector fields on M.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 121 , March 1991 , pp. 127 - 135
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1991

References

[K-N] Kobayashi, S. and Nomizu, K., Foundations of Differential Geometry, vol II, John Wiley, New York (1969).Google Scholar
[N-Pi] Nomizu, K. and Pinkall, P., On the geometry of affine immersions Math. Z., 195 (1987), 165–178.Google Scholar
[N-Pi-Po] Nomizu, K., Pinkall, U. and Podestà, F., On the geometry of affine Kähler immersions, Nagoya Math. J., 120 (1990), 205–222.Google Scholar
[N-S] Nomizu, K. and Smyth, B., Differential geometry for complex hypersurfaces, II J. Math. Soc. Japan, 20 (1968), 498–521.Google Scholar
[S] Smyth, B., Differential geometry of complex hypersurfaces, Ann. of Math., (1967), 246–266.CrossRefGoogle Scholar
[Y] Yano, K., Differential Geometry on Complex and Almost Complex Spaces, Pergamon Press, Oxford (1965).Google Scholar