Geodesic
Functions pluriharmonic on a maniford
Izvestiya. Mathematics, Tome 12 (1978) no. 3, pp. 439-447 
V. K. Beloshapka. Functions pluriharmonic on a maniford. Izvestiya. Mathematics, Tome 12 (1978) no. 3, pp. 439-447. http://geodesic.mathdoc.fr/item/IM2_1978_12_3_a0/
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     author = {V. K. Beloshapka},
     title = {Functions pluriharmonic on a~maniford},
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     volume = {12},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1978_12_3_a0/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $u$ be a smooth function on a manifold $M$. In this paper necessary and sufficient conditions are obtained for $u$ to be the real part of a $CR$-function on $M$. These conditions comprise a system of linear differential equations in this function, whose order depends on the location of $M$ with respect to the complex structure. Bibliography: 8 titles.

[1] Shabat B. V., Vvedenie v kompleksnyi analiz, ch. II, Nauka, M., 1976 | MR

[2] Bedford E., “The Dirichlet problem for some overdetermined system on the unit ball in $\mathbf C^n$”, Pacific J. Math., 51:1 (1974), 312–337 | MR

[3] Lavill G., “Sur les diviseurs de la class de Nevanlinna dans la boul de $\mathbf C^2$”, Comptes Rendus, 281:4 (1975), 145–169 | MR

[4] Bedford E., Federbush P., “Pluriharmonic boundary values”, Tôhoku Math. J., 26 (1974), 76–81 | DOI | MR

[5] Sternberg S., Lektsii po differentsialnoi geometrii, Mir, M., 1970 | MR | Zbl

[6] Nomidzu K., Gruppy Li i differentsialnaya geometriya, IL, M., 1960

[7] Chern S. S., Moser J. K., “Real hypersurfaces in complex manifolds”, Acta Math., 133 (1974), 219–271 | DOI | MR

[8] Tumanov A. E., “O granichnykh znacheniyakh golomorfnykh funktsii neskolkikh kompleksnykh peremennykh”, Uspekhi matem. nauk, 29:4 (1974), 158–159