1,720,962 research outputs found
Classification of maximal transitive prolongations of super-Poincaré algebras
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On the topology of minimal orbits in complex flag manifolds
No full textWe compute the Euler-Poincare characteristic of the homogeneous compact manifolds that can be described as minimal orbits for the action of a real form in a complex flag manifold
Complex vector fields and hypoelliptic partial differential operators
Full text linkWe prove a subelliptic estimate for systems of complex vector fields under some assumptions that generalize the essential pseudoconcavity for CR manifolds, that was first introduced by two of the authors, and the Hörmander's bracket condition for real vector fields. Applications are given to prove the hypoellipticity of first order systems and second order partial differential operators. Finally we describe a class of compact homogeneous CR manifolds for which the distribution of vector fields satisfies a subelliptic estimate
Holomorphic extension from weakly pseudoconcave CR manifolds
No full textThe goal of the paper is to improve known sufficient conditions on a generic CR manifold for local holomorphic extensions of CR functions to a full neighbourhood of a point . Conditions of this kind date back to the important extension result of {\it J. M. Trépreau} [Invent. Math. 83, 583--592 (1986; Zbl 0586.32016)] on monolateral extension of CR functions on a class hypersurface . A known sufficient condition is strict pseudoconvexity of , i.e., the Levi form of has at least one negative eigenvalue in each conormal direction. The general problem of characterizing weakly pseudoconcave manifolds which admit full local extensions is still far from being completely solved. Some sufficient conditions (sector and ray property) are known for weakly pseudoconcave hypersurfaces of finite type. In this paper, the higher codimension case is taken under consideration showing that the situation is much richer than in codimension one. A CR manifold is said to be trace pseudoconcave at a point if, for every (the holomorphic tangent), the Levi form is either zero or has eigenvalues of both signs. Thus trace pseudoconcavity is a condition stronger than weak pseudoconcavity and weaker than strong pseudoconcavity [see {\it C. D. Hill} and {\it M. Nacinovich}, Invent. Math. 142, No. 2, 251--283 (2000; Zbl 0973.32018)]. Let be the sheaf of sections of the holomorphic tangent (i.e., smooth germs of CR vector fields), and let , , be defined as the sheaf generated by and . is said to be of kind at if is the smallest for which the evaluation of at is the tangent space . is said to satisfy the constant rank condition if is independent of . The main result of the paper is the following: Let be a smooth generic CR manifold and . Assume that in a neighbourhood of is trace pseudoconvex, satisfies the constant rank condition and is of kind . Then for every open neighbourhood in , there is an open neighbourhood in such that every CR distribution on is smooth on and has a unique holomorphic extension to . The authors conjecture that the main theorem extends to arbitrary finite kind. The paper is devoted to the proof of the main theorem and to various applications, extensions of the theorem and examples
The CR structure of minimal orbits in complex flag manifolds
No full textLet be a real form of a complex semisimple Lie group Gˆ, P⊂Gˆ a parabolic subgroup and V=Gˆ/P the corresponding flag manifold of Gˆ. As was shown by J. A. Wolf in [Bull. Amer. Math. Soc. 75 (1969), 1121--1237; MR0251246 (40 #4477)], there exists exactly one G-orbit M on V that is closed (and hence compact) in V. This orbit is connected, of minimal dimension amongst the G-orbits and it is naturally endowed with a G-invariant CR structure, namely the one induced by the Gˆ-invariant complex structure of V. Let us call a homogeneous CR manifold which occurs as a closed orbit of this kind a minimal parabolic orbit. Observe that any minimal parabolic orbit M is (up to equivalences) uniquely determined just by a pair (G,P), where G is a real form of a complex semisimple Lie group Gˆ and P is a parabolic subgroup of Gˆ.
The authors single out a set of properties satisfied by the pairs of Lie algebras (\germ g={\rm Lie}(G),\germ p={\rm Lie}(P))(g=Lie(G),p=Lie(P)) associated with minimal parabolic orbits and prove that, conversely, any pair satisfying such properties (called an effective minimal parabolic CR algebra) is associated with a minimal parabolic orbit in some flag manifold.
After this, they show that for a fixed real semisimple Lie algebra \germ gg, the effective minimal parabolic CR algebras of the form (\germ g,\germ p)(g,p) are in one-to-one correspondence with a special class of cross-markings of the Satake diagram of \germ gg. Then, they study some topological properties of the homogeneous CR manifolds associated with effective minimal parabolic CR algebras and give complete characterizations of those, whose associated minimal parabolic orbits satisfy some special conditions on their CR structure. Such characterizations determine immediately new families of examples of CR manifolds that are either CR separable or of finite type or that satisfy nondegeneracy conditions of various kinds
Orbits of real forms in complex flag manifolds
Full text linkThe authors study the structure and the CR geometry of the orbits of a real form of a complex semisimple Lie group in a complex flag manifold . It is shown that any such orbit has a tower of fibrations over a canonically associated real flag manifold with fibers that are products of Euclidean complex spaces and open orbits in complex flag manifolds. This result is used to investigate some topological properties of . For example, it is proved that the fundamental group depends only on and on the conjugacy class of the maximally noncompact Cartan subgroups of the isotropy of the action of on . In particular, the fundamental group of a closed orbit is isomorphic to that of . Many other deep results about properties of the CR structure of the orbits and its invariants and about -equivarant maps between orbits are obtained
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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