Geodesic
The hartogs phenomenon for holomorphically convex Kähler manifolds
Izvestiya. Mathematics, Tome 29 (1987) no. 1, pp. 225-232 
S. M. Ivashkovich. The hartogs phenomenon for holomorphically convex Kähler manifolds. Izvestiya. Mathematics, Tome 29 (1987) no. 1, pp. 225-232. http://geodesic.mathdoc.fr/item/IM2_1987_29_1_a12/
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     title = {The hartogs phenomenon for holomorphically convex {K\"ahler} manifolds},
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is said that the Hartogs phenomenon occurs for a complex manifold $Y$ if every holomorphic mapping $f$ of a domain $D$ over $\mathbf C^n$ into $Y$ extends to a holomorphic mapping $\widetilde f$ of the envelope of holomorphy $\widetilde D$ into $Y$. In this paper it is proved that a holomorphically convex Kähler manifold $Y$ exhibits the Hartogs phenomenon if and only if $Y$ contains no rational curves. Bibliography: 10 titles.

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