On Cauchy-Riemann circle bundles
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- Ciampa Donato Antonio
- POLITECNICO DI TORINO DIMAT DIPARTIMENTO DI MATEMATICA
抄録
Building on ideas of R. Mizner, [17]-[18], and C. Laurent-Thiébaut, [14], we study the CR geometry of real orientable hypersurfaces of a Sasakian manifold. These are shown to be CR manifolds of CR codimension two and to possess a canonical connection D (parallelizing the maximally complex distribution) similar to the Tanaka-Webster connection (cf. [21]) in pseudohermitian geometry. Examples arise as circle subbundles S1→N\stackrel{π}{→}M, of the Hopf fibration, over a real hypersurface M in the complex projective space. Exploiting the relationship between the second fundamental forms of the immersions N→S2n+1 and M→CPn and a horizontal lifting technique we prove a CR extension theorem for CR functions on N. Under suitable assumptions [RicD(Z, \bar{Z})+2g(Z, (I−a)\bar{Z})≥0, Z∈T1, 0(N), where a is the Weingarten operator of the immersion N→S2n+1] on the Ricci curvature RicD of D, we show that the first Kohn-Rossi cohomology group of M vanishes. We show that whenever RicD(Z, \bar{W})−2g(Z, \bar{W})=(μ{\circ}π)g(Z, \bar{W}) for some μ∈C∞(M), M is a pseudo-Einstein manifold.
収録刊行物
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- KODAI MATHEMATICAL JOURNAL
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KODAI MATHEMATICAL JOURNAL 28 (1), 146-180, 2005
国立大学法人 東京工業大学理学院数学系
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詳細情報 詳細情報について
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- CRID
- 1390001205271641344
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- NII論文ID
- 130003574475
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- ISSN
- 18815472
- 03865991
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- MRID
- 2122197
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- en
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- JaLC
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