Deformations of a complex manifold near a strongly pseudo-convex real hypersurface and a realization of Kuranishi family of strongly pseudo-convex CR structures

1990 ◽  
Vol 205 (1) ◽  
pp. 593-602 ◽  
Author(s):  
Kimio Miyajima
Keyword(s):  
Complex Manifold ◽  
Real Hypersurface ◽  
Pseudo Convex ◽  
Cr Structures

scholarly journals Local deformations of isolated singularities associated with negative line bundles over abelian varieties

1979 ◽  
Vol 75 ◽  
pp. 41-70
Author(s):  
Hideo Omoto ◽  
Shigeo Nakano
Keyword(s):  
Complex Manifold ◽  
Real Hypersurface ◽  
Abelian Varieties ◽  
Analytic Space ◽  
Line Bundles ◽  
Isolated Singularity ◽  
Isolated Singularities ◽  
Universality Theorem ◽  
Pseudo Convex ◽  
Local Deformations

Let V be an analytic space with an isolated singularity p. In [1] M. Kuranishi approached the problem of deformations of isolated singularities (c.f. [2] and [3]) as follows; Let M be a real hypersurface in the complex manifold V − {p}. Then one has the induced CR-structure °T″(M) on M by the inclusion map i: M→ V − {p} (c.f. Def. 1.6). Then deformations of the isolated singularity (V, p) give rise to ones of the induced CR-structure °T″(M). He established in §9 in [1] the universality theorem for deformations of the induced CR-structure °T″(M)9 when M is compact strongly pseudo-convex (Def. 1.5) of dim M ≧ 5. Form this theorem we can know CR-structures on M which appear in deformations of °T″(M).

scholarly journals Non-degenerate real hypersurfaces in complex manifolds admitting large groups of pseudo-conformal transformations. I

1976 ◽  
Vol 62 ◽  
pp. 55-96 ◽  
Author(s):  
Keizo Yamaguchi
Keyword(s):  
Complex Manifold ◽  
Real Hypersurface ◽  
Levi Form ◽  
Real Hypersurfaces ◽  
Conformal Transformations ◽  
Complex Manifolds ◽  
Real Analytic ◽  
Large Groups

Let S (resp. S′) be a (real) hypersurface (i.e. a real analytic sub-manifold of codimension 1) of an n-dimensional complex manifold M (resp. M′). A homeomorphism f of S onto S′ is called a pseudo-conformal homeomorphism if it can be extended to a holomorphic homeomorphism of a neighborhood of S in M onto a neighborhood of S′ in M. In case such an f exists, we say that S and S′ are pseudo-conformally equivalent. A hypersurface S is called non-degenerate (index r) if its Levi-form is non-degenerate (and its index is equal to r) at each point of S.

scholarly journals Nonexistence of real analytic Levi flat hypersurfaces in ℙ2

2000 ◽  
Vol 158 ◽  
pp. 95-98 ◽  
Author(s):  
Takeo Ohsawa
Keyword(s):  
Complex Manifold ◽  
Real Hypersurface ◽  
Real Analytic

AbstractA real hypersurface M in a complex manifold X is said to be Levi flat if it separates X locally into two Stein pieces. It is proved that there exist no real analytic Levi flat hypersurfaces in ℙ2.

scholarly journals On Realizations of Families of Strongly Pseudo-Convex CR Structures

1992 ◽  
Vol 15 (1) ◽  
pp. 153-170 ◽  
Author(s):  
Kimio MIYAJIMA
Keyword(s):  
Pseudo Convex ◽  
Cr Structures

SOLUTION TO $\overline{\partial}$-EQUATIONS WITH EXACT SUPPORT ON PSEUDO-CONVEX MANIFOLDS

2007 ◽  
Vol 04 (03) ◽  
pp. 339-348 ◽  
Author(s):  
OSAMA ABDELKADER ◽  
SAYED SABER
Keyword(s):  
Vector Bundle ◽  
Complex Manifold ◽  
Smooth Boundary ◽  
Holomorphic Vector Bundle ◽  
Property B ◽  
Pseudo Convex ◽  
Complex Valued ◽  
Satisfying Property

We obtain a solution to the [Formula: see text]-equation with exact support in a domain Ω with C1-smooth boundary satisfying property B in a complex manifold. This is done for complex-valued forms of type (r,s), s ≥ 1 and for forms of type (r,s), q ≤ s ≤ n - q, with values in a holomorphic vector bundle when the domain Ω is strongly q-convex.

A Note on the Analogue of the Bogomolov Type Theorem on Deformations of CR-Structures

1994 ◽  
Vol 37 (1) ◽  
pp. 8-12 ◽  
Author(s):  
Takao Akahori ◽  
Kimio Miyajima
Keyword(s):  
Line Bundle ◽  
Type Theorem ◽  
Strict Sense ◽  
Weak Version ◽  
Cr Manifold ◽  
Canonical Line Bundle ◽  
Pseudo Convex ◽  
Cr Structures

AbstractLet (M, °T″) be a compact strongly pseudo-convex CR-manifold with trivial canonical line bundle. Then, in [A-M2], a weak version of the Bogomolov type theorem for deformations of CR-structures was shown by an analogy of the Tian- Todorov method. In this paper, we show that: in the very strict sense, there is a counterexample.

A SMOOTHNESS OF DEFORMATIONS OF NORMAL STRONGLY PSEUDO-CONVEX CR-STRUCTURES

1998 ◽  
Vol 52 (2) ◽  
pp. 413-438
Author(s):  
Takao AKAHORI ◽  
Kimio MIYAJIMA
Keyword(s):  
Pseudo Convex ◽  
Cr Structures
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