an:04147116
Zbl 0699.58002
Eliashberg, Yakov
Topological characterization of Stein manifolds of dimension \(>2\)
EN
Int. J. Math. 1, No. 1, 29-46 (1990).
00155504
1990
j
58A05 58E05 32E10 53C15
topological characterization of Stein manifolds; smooth manifold; almost complex structure
In this paper is given a topological characterization of Stein manifolds of dimension \(>2.\)
The main result is the following: Let X be a 2n-dimensional smooth manifold, \(n>2\), with an almost complex structure J and assume that there exists a proper Morse function \(\phi\) : \(X\to {\mathbb{R}}\) such that the indexes of all its critical points are \(\leq n\). Then there exists a complex structure \(\tilde J\) on X such that \((X,\tilde J)\) is Stein. In fact the author shows that the new structure \(\tilde J\) can be chosen such that J is homotopic to \(\tilde J\) and \(\phi\) is \(\tilde J\)-convex. By a well-known result of Grauert \((X,\tilde J)\)is Stein.
M.Col??oiu