“ON STRONGLY q-PSEUDOCONVEX SPACES WITH POSITIVE VECTOR BUNDLES”

Eto, Shun‐ichi; Kazama, Hideaki; Watanabe, Kiyoshi

doi:10.2206/kyushumfs.28.135

Cited by 5 publications

(4 citation statements)

References 10 publications

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“…The embeddable 1-convex spaces. The first result in this direction in the nonsingular case was established in [1].…”

mentioning

confidence: 96%

“…Theorem 1 [1]. Let X be a l-convex manifold and let us assume that there exists a positive line bundle L on X.…”

mentioning

confidence: 99%

“…By slightly modifying the proof in [1] and by using some standard techniques, we shall generalize Theorem 1 in two directions. First of all we do not require X to be nonsingular, and secondly the line bundle L does not need to be positive on the whole space X.…”

mentioning

confidence: 99%

“…Actually in [0] (see also [1]), the previous result was proved for ^-convex spaces, for any q > 1. However, in the special case of 1-convex spaces, Theorem 2 can be sharpened as follows.…”

mentioning

confidence: 99%

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On the embedding problem for 1-convex spaces

Tan¹

1979

Trans. Amer. Math. Soc.

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“…The embeddable 1-convex spaces. The first result in this direction in the nonsingular case was established in [1].…”

mentioning

confidence: 96%

“…Theorem 1 [1]. Let X be a l-convex manifold and let us assume that there exists a positive line bundle L on X.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

“…Actually in [0] (see also [1]), the previous result was proved for ^-convex spaces, for any q > 1. However, in the special case of 1-convex spaces, Theorem 2 can be sharpened as follows.…”

mentioning

confidence: 99%

See 2 more Smart Citations

On the embedding problem for 1-convex spaces

Tan¹

1979

Trans. Amer. Math. Soc.

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Sur les fibres infinitesimales d'un morphisme propre d'espaces complexes

Bănică¹

1980

Lecture Notes in Mathematics

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Kähler–Einstein metrics on strictly pseudoconvex domains

Coevering

2012

Ann Glob Anal Geom

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Extending the results of S. Y. Cheng and S.-T. Yau it is shown that a strictly pseudoconvex domain M ⊂ X in a complex manifold carries a complete Kähler-Einstein metric if and only if its canonical bundle is positive, i.e. admits an Hermitian connection with positive curvature. We consider the restricted case in which the CR structure on ∂M is normal. In this case M must be a domain in a resolution of the Sasaki cone over ∂M . We give a condition on a normal CR manifold which it cannot satisfy if it is a CR infinity of a Kähler-Einstein manifold. We are able to mostly determine those normal CR 3-manifolds which can be CR infinities.We give many examples of Kähler-Einstein strictly pseudoconvex manifolds on bundles and resolutions. In particular, the tubular neighborhood of the zero section of every negative holomorphic vector bundle on a compact complex manifold whose total space satisfies c 1 < 0 admits a complete Kähler-Einstein metric.

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“ON STRONGLY q-PSEUDOCONVEX SPACES WITH POSITIVE VECTOR BUNDLES”

Cited by 5 publications

References 10 publications

On the embedding problem for 1-convex spaces

On the embedding problem for 1-convex spaces

Sur les fibres infinitesimales d'un morphisme propre d'espaces complexes

Kähler–Einstein metrics on strictly pseudoconvex domains

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