We consider an alternative approach to a fundamental CR invariant – the Catlin multitype. It is applied to a general smooth hypersurface in C, not necessarily pseudoconvex. Using this approach, we prove biholomorphic equivalence of models, and give an explicit description of biholomorphisms between different models. A constructive finite algorithm for computing the multitype is described. The r...

The Kobayashi indicatrix (infinitesimal unit ball) of a domain in IE n is known to be a biholomorphic invariant. In particular, if a domain is biholomorphic to a ball, then the indicatrix is the ball. Until the recent deep results of Lempert [4], it was not known to what extent the indicatrix characterizes the domain. Sibony had shown earlier that the indicatrix of any pseudoconvex circular dom...

Any (global) kähler deformation of a flag manifold F with b2 = 1 is biholomorphic to F .

In the paper [SY80] it was shown that a Kähler manifold with strictly positive bisectional curvature was biholomorphic to CP. In this paper, we use the techniques developed by [SY80], to prove that a compact Kähler manifold with positive orthogonal bisectional curvature is biholomorphic to CP, a condition strictly weaker than positive bisectional curvature. This gives a direct elliptic proof of...

In this paper we discuss some connections between proper holomorphic mappings between domains in Cn and the boundary behaviors of certain canonical invariant metrics. A compactness theorem has been proved. This generalizes slightly an earlier result proved by the second author. Introduction. A continuous mapping f:Xx —* X2 between two topological spaces is called proper if f~l(K) c X\ is compac...

We study isometries of the Kobayashi and Carathéodory metrics on strongly pseudoconvex and strongly convex domains in C and prove: (i) Let Ω1 and Ω2 be strongly pseudoconvex domains in C and f : Ω1 → Ω2 an isometry. Suppose that f extends as a C map to Ω̄1. Then f |∂Ω1 : ∂Ω1 → ∂Ω2 is a CR or anti-CR diffeomorphism. Hence it follows that Ω1 and Ω2 must be biholomorphic or anti-biholomorphic. (ii)...

We exhibit a locally biholomorphic mapping with simply connected image, which fails to be a topological covering. Introduction In [1], A.F.Beardon shows an example of a ’covering surface’ over the unit disc D ⊂ C, which is not a topological covering. We recall that a ’covering surface’ of a regionD ⊂ C, is a Riemann surface S admitting surjective conformal mapping onto D, whereas a continuous m...

Any (global) deformation of a flag manifold F with b2 = 1 is biholomorphic to F .

In this paper, our interest is devoted to study the convex combinations of form (1 ? ?) f + ?1, where (0, 1), biholomorphic mappings on Euclidean unit ball Bn in case several complex variables. Starting from a result proved by S. Trimble [26] and then extended P.N. Chichra R. Singh [3, Theorem 2] which says that if starlike such Re[f ?(z)] > 0, (1??)z+?f (z) also starlike, we are interested ...

Here R+ denotes the upper half-plane and BMO(R 2 +×R 2 +) is defined to be the dual of the realvariable Hardy space H on the product domain R+×R 2 +. There are several equivalent ways to define this latter space and the reader is referred to [5] for the various characterizations. We will be more interested in the biholomorphic analogue of H, which can be defined in terms of the boundary values ...