1,720,959 research outputs found
Bott–Chern harmonic forms and primitive decompositions on compact almost Kähler manifolds
No full textLet (X, J, ?) be a compact 2n-dimensional almost Kahler manifold. We prove primitive decompositions for Bott-Chern and Aeppli harmonic forms in special bidegrees and show that such bidegrees are optimal. We also show how the spaces of primitive Bott-Chern, Aeppli, Dolbeault and ?-harmonic forms on (X, J, ?) are related
Aeppli Cohomology and Gauduchon Metrics
No full textLet (M, J, g, ω) be a complete Hermitian manifold of complex dimension n≥ 2. Let 1 ≤ p≤ n- 1 and assume that ωn-p is (∂+ ∂ ̄) -bounded. We prove that, if ψ is an L2 and d-closed (p, 0)-form on M, then ψ= 0. In particular, if M is compact, we derive that if the Aeppli class of ωn-p vanishes, then HBCp,0(M)=0. As a special case, if M admits a Gauduchon metric ω such that the Aeppli class of ωn-1 vanishes, then HBC1,0(M)=0
Bott–Chern Laplacian on almost Hermitian manifolds
Full text linkLet (M, J, g, ω) be a 2n-dimensional almost Hermitian manifold. We extend the definition of the Bott–Chern Laplacian on (M, J, g, ω) , proving that it is still elliptic. On a compact Kähler manifold, the kernels of the Dolbeault Laplacian and of the Bott–Chern Laplacian coincide. We show that such a property does not hold when (M, J, g, ω) is a compact almost Kähler manifold, providing an explicit almost Kähler structure on the Kodaira–Thurston manifold. Furthermore, if (M, J, g, ω) is a connected compact almost Hermitian 4-manifold, denoting by hBC1,1 the dimension of the space of Bott–Chern harmonic (1, 1)-forms, we prove that either hBC1,1=b- or hBC1,1=b-+1. In particular, if g is almost Kähler, then hBC1,1=b-+1, extending the result by Holt and Zhang (Harmonic forms on the Kodaira–Thurston manifold. arXiv:2001.10962, 2020) for the kernel of Dolbeault Laplacian. We also show that the dimensions of the spaces of Bott–Chern and Dolbeault harmonic (1, 1)-forms behave differently on almost complex 4-manifolds endowed with strictly locally conformally almost Kähler metrics. Finally, we relate some spaces of Bott-Chern harmonic forms to the Bott–Chern cohomology groups for almost complex manifolds, recently introduced in Coelho et al. (Maximally non-integrable almost complex structures: an h-principle and cohomological properties, arXiv:2105.12113, 2021)
On the dimension of Dolbeault harmonic (1, 1)-forms on almost Hermitian 4-manifolds
No full textWe prove that the dimension h1,1 of the space of Dol-beault harmonic (1, 1)-forms is not necessarily always equal to b− ∂ on a compact almost complex 4-manifold endowed with an almost Hermitian metric which is not locally conformally almost Kähler. Indeed, we provide examples of non integrable, non locally con-formally almost Kähler, almost Hermitian structures on compact 4-manifolds with h1,1 = b−+1. This gives an answer to [6, Question ∂ 3.3] by Holt
Bott-Chern harmonic forms on complete Hermitian manifolds
No full textLet (M, J, g,ω) be a Hermitian manifold of complex dimension n. Assume that the torsion of the Chern connection Δ is bounded, and that there exists a C∞exhausting function ρ : M → R such that Δρ,Δ2ρ are bounded. We characterize W1,2 Bott-Chern harmonic forms, extending the usual result that holds on compact Hermitian manifolds. Finally, if (M,J, g,ω) is Kähler complete, ω = dη, with η bounded, and the sectional curvature is bounded, then we get a vanishing theorem for W1,2 Bott-Chern harmonic (p, q)-forms, if p + q ≠= n
Invariants of almost complex and almost Kähler manifolds
No full textGiven a compact almost complex manifold (M-2n,J), the almost complex invariant h(J)(p,q) is defined as the complex dimension of the cohomology space {[alpha] is an element of H-dR(p+q)(M-2n; C)|alpha is an element of A(p,q)(M-2n),d alpha = 0}. Its properties have been studied mainly when 2n = 4. If we endow (M2n,J) with an almost Hermitian metric g, then the number h(d)(p,q), i.e. the complex dimension of the space of Hodge-de Rham harmonic (p,q)-forms, does not depend on the choice of almost Kahler metrics when 2n = 4. In this paper, we study the relationship between h(J)(p,q) and h(d)(p,q) in dimension 2n >= 4. We prove hJn,0 = 0 if J is non-integrable and observe that h(d)(p,0) = h(J)(p,0) if the metric is almost Kahler. If M-2n is a compact quotient of a completely solvable Lie group and (J,g,omega) is a left-invariant almost Kahler structure on M, we prove h(d)(1,1) = h(J)(1,1). Finally, we study the C-infinity-pure and C-infinity-full properties of J on n-forms for the special dimension 2n = 4m
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
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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