Geodesic
Remarks on k-Leviflat Complex Manifolds
Canadian journal of mathematics, Tome 31 (1979) no. 4, pp. 881-889

Voir la notice de l'article provenant de la source Cambridge University Press

In the theory of functions of several complex variables one is naturally led to study non-compact complex manifolds which have certain types of exhaustions. For example, on a Stein manifold X there is a strictly plurisubharmonic function φ: X → R+ so that the pseudoballs Bc = {φ < c } exhaust X. Conversely, a manifold which has such an exhaustion is Stein. The purpose of this note is to study a class of manifolds which have exhaustions along the lines of those on holomorphically convex manifolds, namely the k-Leviflat complex manifolds. Unlike the Stein case, the Levi form may have positive dimensional 0-eigenspaces. In the holomorphically convex case these are tangent to the generic fiber of the Remmert reduction. 
Gilligan, B.; Huckleberry, A. Remarks on k-Leviflat Complex Manifolds. Canadian journal of mathematics, Tome 31 (1979) no. 4, pp. 881-889. doi: 10.4153/CJM-1979-083-1
@article{10_4153_CJM_1979_083_1,
     author = {Gilligan, B. and Huckleberry, A.},
     title = {Remarks on {k-Leviflat} {Complex} {Manifolds}},
     journal = {Canadian journal of mathematics},
     pages = {881--889},
     year = {1979},
     volume = {31},
     number = {4},
     doi = {10.4153/CJM-1979-083-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1979-083-1/}
}
TY  - JOUR
AU  - Gilligan, B.
AU  - Huckleberry, A.
TI  - Remarks on k-Leviflat Complex Manifolds
JO  - Canadian journal of mathematics
PY  - 1979
SP  - 881
EP  - 889
VL  - 31
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1979-083-1/
DO  - 10.4153/CJM-1979-083-1
ID  - 10_4153_CJM_1979_083_1
ER  - 
%0 Journal Article
%A Gilligan, B.
%A Huckleberry, A.
%T Remarks on k-Leviflat Complex Manifolds
%J Canadian journal of mathematics
%D 1979
%P 881-889
%V 31
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1979-083-1/
%R 10.4153/CJM-1979-083-1
%F 10_4153_CJM_1979_083_1

[1] 1. Diederich, K. and Fornaess, J. E., Pseudoconvex domains: Bounded strictly plurisubharmonic exhaustion functions, Inv. Math. 89 (2) (1977), 129–141. Google Scholar

[2] 2. Freeman, M., Local complex foliations of real submanifolds, Math. Ann. 209 (1974), 1–30. Google Scholar

[3] 3. Gilligan, B. and Huckleberry, A., On non-compact complex nil-manifolds , (to appear). Google Scholar

[4] 4. Grauert, H., On Levi s problem and the imbedding of real-analytic manifolds, Ann. Math. 68 (1958), 460–472. Google Scholar

[5] 5. Grauert, H., Die Bedeutung des Levischen Problems fur die analytische und algebraische Géométrie, Pro. Int. Cong. Math. Stockholm (1962), 86–101. Google Scholar

[6] 6. Green, M., Holomorphic maps into complex tori , (to appear in Amer. J. of Math.) Google Scholar

[7] 7. Huckleberry, A., The Levi problem on pseudoconvex manifolds which are not strongly pseudoconvex, Math. Ann. 219 (1976), 127–137. Google Scholar

[8] 8. Huckleberry, A., Holomorphic fibrations of bounded domains, Math. Ann. 227 (1977), 61–66. Google Scholar

[9] 9. Huckleberry, A. and Nirenberg, R., On k-pseudoflat complex spaces, Math. Ann. 200 (1973), 1–10. Google Scholar

[10] 10. Kazama, H., On pseudoconvexity of complex abelian Lie groups, J. Math. Soc. Japan, 25 (2) (1973), 329–333. Google Scholar

[11] 11. Kobayashi, S., Hyperbolic manifolds and holomorphic mappings (Marcel Dekker, Inc., New York, 1970). Google Scholar

[12] 12. Matsushima, Y., On the discrete subgroups and homogeneous spaces of nilpotent Lie groups, Nagoya Math. J. 2 (1951), 95–110. Google Scholar

[13] 13. Morimoto, A., Non-compact complex Lie groups without non-constant holomorphic functions, Proceedings of the Conference on Complex Analysis, Minneapolis (1964), 256–272. Google Scholar

[14] 14. Stein, K., Analytische Zerlegungen komplexer Rdmne, Math. Ann. 182 (1956), 63–93. Google Scholar

Cité par Sources :