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Some applications of Synge’s formula to the theory of several complex variables

Published online by Cambridge University Press:  22 January 2016

Takeshi Sasaki  and
Osamu Suzuki
Takeshi Sasaki
Affiliation:
Nagoya University and Nihon University
Osamu Suzuki
Affiliation:
Nagoya University and Nihon University
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In [10] and [11], the second author proved the following theorem by using Synge’s formula:

THEOREM I. Let M be a kähler manifold with positive holomorphic bi-sectional curvature. Then every pseudoconvex domain in M is a Stein manifold.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 67 , August 1977 , pp. 53 - 64
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1977

References

[1] Bishop, R. L. and Crittenden, R. J., Geometry of Manifolds, Academic Press, New York, 1964.Google Scholar
[2] Cheeger, R. I. and Gromoll, R., On the structure of complete manifolds of non-negative curvature, Ann. of Math. 96 (1974), 414–443.Google Scholar
[3] Goldberg, S. I. and Kobayashi, S.: On holomorphic bisectional curvature, J. Diff. Geometry 1 (1967), 225–233.Google Scholar
[4] Grauert, H., Über Modifikationen und die exzeptionelle analytische Mengen, Math. Ann. 146 (1962), 331–368.Google Scholar
[5] Grauert, H., Bemerkenswerte pseudokonvexe Mannigfaltigkeiten, Math. Zeit. 81 (1964), 377–391.Google Scholar
[6] Greene, R. E. and Wu, H., On the subharmonicity and plurisubharmonicity of geodesically convex functions, Indiana Univ. Math. J. 22 (1973), 641–653.Google Scholar
[7] Greene, R. E. and Wu, H., Approximation theorems, C∞-convex exhaustions and manifolds of positive curvature, Bull. Amer. Math. Soc. 81 (1975), 101–104.Google Scholar
[8] Gromoll, R. and Meyer, W., On complete open manifolds of positive curvature, Ann. of Math. 90 (1969), 75–90.Google Scholar
[9] Hermann, R., Convexity and pseudoconvexity for complex manifolds, J. Math. Mech. 13 (1964), 667–672.Google Scholar
[10] Suzuki, O., Pseudoconvex domains on a kähler manifold with positive holomorphic bisectional curvature, to appear in Publ. Res. Inst. Math. Sci., 12.Google Scholar
[11] Suzuki, O., Supplement to “Pseudoconvex domains on a kähler manifold with positive holomorphic bisectional curvature”, to appear in Publ. Res. Inst. Math. Sci., 12.Google Scholar
[12] Takeuchi, A., Domains pseudoconvexes sur les variétés kähleriennes, J. Math. Kyoto Univ. 6-3 (1967), 323–357.Google Scholar
[13] Wu, H., Negatively curved kähler manifolds, Notices Amer. Math. Soc. 14 (1967), 515.Google Scholar