1,721,143 research outputs found
On the geometric order of totally nondegenerate CR manifolds
Full text linkA CR manifold M, with CR distribution D10⊂ TCM, is called totally nondegenerate of depthμ if: (a) the complex tangent space TCM is generated by all complex vector fields that might be determined by iterated Lie brackets between at most μ fields in D10+ D10 ̄ ; (b) for each integer 2 ≤ k≤ μ- 1 , the families of all vector fields that might be determined by iterated Lie brackets between at most k fields in D10+ D10 ̄ generate regular complex distributions; (c) the ranks of the distributions in (b) have the maximal values that can be obtained amongst all CR manifolds of the same CR dimension and satisfying (a) and (b)—this maximality property is the total nondegeneracy condition. In this paper, we prove that, for any Tanaka symbol m= m-μ+ ⋯ + m- 1 of a totally nondegenerate CR manifold of depth μ≥ 4 , the full Tanaka prolongation of m has trivial subspaces of degree k≥ 1 , i.e. it has the form m-μ+ ⋯ + m- 1+ g. This result has various consequences. For instance it implies that any (local) CR automorphism of a regular totally nondegenerate CR manifold is uniquely determined by its first order jet at a fixed point of the manifold. It also gives a complete proof of a conjecture by Beloshapka on the group of automorphisms of homogeneous totally nondegenerate CR manifolds
Instantons on hyperkähler manifolds
Full text linkAn instanton on a (pseudo-)hyperk\"ahler manifold is a vector bundle associated to a principal -bundle with a connection whose curvature is pointwise invariant under the quaternionic structures of , and thus satisfies the Yang-Mills equations. Revisiting a construction of solutions, we prove a local bijection between gauge equivalence classes of instantons on and equivalence classes of certain holomorphic functions taking values in the Lie algebra of defined on an appropriate -bundle over . Our reformulation affords a streamlined proof of Uhlenbeck's Compactness Theorem for instantons on (pseudo-)hyperk\"ahler manifolds
Hyperkähler cones and instantons on quaternionic Kähler manifolds
Full text linkWe present a novel approach to the study of Yang-Mills instantons on quaternionic Kähler manifolds, based on an extension of the harmonic space method of constructing instantons on hyperk\"ahler manifolds. Our results establish a bijection between local equivalence classes of instantons on quaternionic Kähler manifolds M and equivalence classes of certain holomorphic maps on an appropriate SL_2(C)-bundle over the Swann bundle of M
Eversive Maps of Bounded Convex Domains in â„‚n+1
No full textA duality principle, relating the geometry of the Kobayashi metric with the CR geometry of the boundaries of smoothly bounded, strongly convex domains in â„‚n+1, is established. A characterization of the holomorphic Jacobi vector fields of those domains is also given
Hyperkähler cones and instantons on quaternionic Kähler manifolds
No full textWe present a novel approach to the study of Yang–Mills instantons on quaternionic Kähler manifolds, based on an extension of the harmonic space method of constructing instantons on hyperkähler manifolds. Our results establish a bijection between local equivalence classes of instantons on quaternionic Kähler manifolds M and equivalence classes of certain holomorphic maps on an appropriate SL 2(C) -bundle over the Swann bundle of M
Propagation of regularity for Monge-Ampère exhaustions and Kobayashi metrics
Full text linkWe prove that if a smoothly bounded strongly pseudoconvex domain D⊂ Cn, n≥ 2 , admits at least one Monge-Ampère exhaustion smooth up to the boundary (i.e., a plurisubharmonic exhaustion τ: D ̄ → [0 , 1] , which is C∞ at all points except possibly at the unique minimum point x and with u: = log τ satisfying the homogeneous complex Monge-Ampère equation), then there exists a bounded open neighborhood U⊂ D of the minimum point x, such that for each y∈ U there exists a Monge-Ampère exhaustion with minimum at y. This yields that for each such domain D, the restriction to the subdomain U⊂ D of the Kobayashi pseudo-metric κD is a smooth Finsler metric for U and each pluricomplex Green function of D with pole at a point y∈ U is of class C∞. The boundary of the maximal open subset having all such properties is also explicitly characterized. The result is a direct consequence of a general theorem on abstract complex manifolds with boundary, with Monge-Ampère exhaustions of regularity Ck for some k≥ 5. In fact, analogues of the above properties hold for each bounded strongly pseudoconvex complete circular domain with boundary of such weaker regularity
Control problems with differential constraints of higher order
Full text linkWe consider cost minimising control problems, in which the dynamical system is constrained by higher order differential equations of Euler–Lagrange type. Following ideas from a previous paper, we prove that a curve of controls uo(t) and a set of initial conditions σo give an optimal solution for a control problem of the considered type if and only if an appropriate double integral is greater than or equal to zero along any homotopy (u(t,s),σ(s)) of control curves and initial data starting from uo(t)=u(t,0) and σo=σ(0). This property is called Principle of Minimal Labour. From this principle we derive a generalisation of the classical Pontryagin Maximum Principle that holds under higher order differential constraints of Euler–Lagrange type and without the hypothesis of fixed initial data
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
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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