Affine Kähler hypersurfaces satisfying certain conditions on the curvature tensor |
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Authors: | Fabio Podestà |
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Institution: | 1. c/o Scuola Normale Superiore, P.zza Cavalieri, 7, I-56100, Pisa
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Abstract: | The notion of affine Kähler immersions has been recently introduced by Nomizu-Pinkall-Podestà (N-Pi-Po]). This work is aimed at giving some results towards the classification of non degenerate affine Kähler hypersurfaces with symmetric and parallel Ricci tensor; this problem generalizes the classical results due to Nomizu-Smyth (N-S]) in the theory of Kählerian hypersurfaces. In a second section we deal with the case of “semisymmetric” affine Kähler immersions, when the curvature tensor R satisfies R · R = 0 and the Ricci tensor is symmetric, providing a complete classification; for affine Kähler curves we prove that the conditions above are actually equivalent to saying that the immersion is isometric for a suitable Kähler metric in C2. |
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