1,720,979 research outputs found
Remarkable Classes of Almost 3-Contact Metric Manifolds
No full textWe introduce a new class of almost 3-contact metric manifolds, called 3-(0,δ)-Sasaki manifolds. We show fundamental geometric properties of these manifolds, analyzing analogies and differences with the known classes of 3-(α,δ)-Sasaki (α≠0) and 3-δ-cosymplectic manifolds
Riemannian almost CR manifolds with torsion
No full textWe characterize and study Riemannian almost CR manifolds admitting characteristic connections, i.e. metric connections with totally skew-symmetric torsion, parallelizing the almost CR structure.
Natural constructions are provided of new non trivial examples. We study the influence of the curvature
of the metric on the underlying almost CR structure. A global classification is obtained under flatness assumption of a characteristic connection, provided that the fundamental 2-form of the structure is closed (quasi Sasakian condition)
A note on Riemannian connections with skew torsion and the de Rham splitting
Full text linkWe prove that a Riemannian manifold admitting a metric connection with totally skew-symmetric torsion and reducible holonomy is locally reducible, provided it has nonpositive sectional curvature
Curvature properties of 3-(α, δ)-Sasaki manifolds
Full text linkWe investigate curvature properties of 3-(α, δ)-Sasaki manifolds, a special class of almost 3-contact metric manifolds generalizing 3-Sasaki manifolds (corresponding to α = δ = 1) that admit a canonical metric connection with skew torsion and define a Riemannian submersion over a quaternionic Kähler manifold with vanishing, positive or negative scalar curvature,
according to δ = 0, αδ > 0 or αδ < 0. We shall investigate both the Riemannian curvature and the curvature of the canonical connection, with particular focus on their curvature operators, regarded as symmetric endomorphisms of the space of 2-forms. We describe their spectrum,
find distinguished eigenforms, and study the conditions of strongly definite curvature in the sense of Thorpe
Homogeneous non-degenerate 3-(α,δ)-Sasaki manifolds and submersions over quaternionic Kähler spaces
Full text linkWe show that every 3-(α, δ) -Sasaki manifold of dimension 4n+ 3 admits a locally defined Riemannian submersion over a quaternionic Kähler manifold of scalar curvature 16n(n+ 2)αδ. In the non-degenerate case we describe all homogeneous 3-(α, δ) -Sasaki manifolds fibering over symmetric Wolf spaces and over their non-compact dual symmetric spaces. If αδ> 0 , this yields a complete classification of homogeneous 3-(α, δ) -Sasaki manifolds. For αδ< 0 , we provide a general construction of homogeneous 3-(α, δ) -Sasaki manifolds fibering over non-symmetric Alekseevsky spaces, the lowest possible dimension of such a manifold being 19
Anti-quasi-Sasakian manifolds
Full text linkWe introduce and study a special class of almost contact metric manifolds, which we call anti-quasi-Sasakian (aqS). Among the class of transversely Kahler almost contact metric manifolds (M, phi, xi, eta, g), quasi-Sasakian and anti-quasi-Sasakian manifolds are characterized, respectively, by the.-invariance and the phi-anti-invariance of the 2-form d eta. A Boothby-Wang type theorem allows to obtain aqS structures on principal circle bundles over Kahler manifolds endowed with a closed (2, 0)-form. We characterize aqS manifolds with constant xi-sectional curvature equal to 1: they admit an Sp(n) x 1-reduction of the frame bundle such that the manifold is transversely hyperkahler, carrying a second aqS structure and a null Sasakian eta-Einstein structure. We show that aqS manifolds with constant sectional curvature are necessarily flat and cokahler. Finally, by using a metric connection with torsion, we provide a sufficient condition for an aqS manifold to be locally decomposable as the Riemannian product of a Kahler manifold and an aqS manifold with structure of maximal rank. Under the same hypothesis, (M, g) cannot be locally symmetric
Odd-dimensional counterparts of abelian complex and hypercomplex structures
Full text linkWe introduce the notion of abelian almost contact structures on an odd-dimensional real Lie algebra g. We investigate correspondences with even-dimensional Lie algebras endowed with an abelian complex structure, and with Kähler Lie algebras when g carries a compatible inner product. The classification of 5-dimensional Sasakian Lie algebras with abelian structure is obtained. Later, we introduce abelian almost 3-contact structures on real Lie algebras of dimension 4n + 3, obtaining the classification of these Lie algebras in dimension 7. Finally, we deal with the geometry of a Lie group G endowed with a left invariant abelian almost 3-contact metric structure. We determine conditions for G to admit a canonical metric connection with skew torsion, which plays the role of the Bismut connection for HKT structures arising from abelian hypercomplex structures. We provide examples and discuss the parallelism of the torsion of the canonical connection
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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