1,721,006 research outputs found
Generalized vector cross products and Killing forms on negatively curved manifolds
No full textMotivated by the study of Killing forms on compact Riemannian manifolds of negative sectional curvature, we introduce the notion of generalized vector cross products on Rn and give their classification. Using previous results about Killing tensors on negatively curved manifolds and a new characterization of SU (3) -structures in dimension 6 whose associated 3-form is Killing, we then show that every Killing 3-form on a compact n-dimensional Riemannian manifold with negative sectional curvature vanishes if n≥ 4.Fil: Barberis, Maria Laura Rita. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaFil: Moroianu, Andrei. Université Paris Sud; FranciaFil: Semmelmann, Uwe. Universität Stuttgart; Alemani
Stability of Einstein metrics on homogeneous spaces
Full text link(1) Stability of Einstein metrics on symmetric spaces of compact type:
We prove the linear stability with respect to the Einstein-Hilbert action of the symmetric spaces SU(n), n ≥ 3, and E_6/F_4 . Combined with earlier results, this resolves the stability problem for irreducible symmetric spaces of compact type.(2) Coindex and rigidity of Einstein metrics on homogeneous Gray manifolds:
Any 6-dimensional strict nearly Kähler manifold is Einstein with positive scalar curvature. We compute the coindex of the metric with respect to the Einstein-Hilbert functional on each of the compact homogeneous examples. Moreover, we show that the infinitesimal Einstein deformations on F_1,2 = SU(3)/T_2 are not integrable into a curve of Einstein metrics.(3) Stability of the Non-Symmetric Space E_7/PSO(8):
We prove that the normal metric on the homogeneous space E_7/PSO(8) is stable with respect to the Einstein-Hilbert action, thereby exhibiting the first known example of a non-symmetric metric of positive scalar curvature with this property.(4) The Lichnerowicz Laplacian on normal homogeneous spaces:
We give a new formula for the Lichnerowicz Laplacian on normal homogeneous spaces in terms of Casimir operators. We derive some practical estimates and apply them to the known list of non-symmetric, compact, simply connected homogeneous spaces G/H with G simple whose standard metric is Einstein. This yields many new examples of Einstein metrics which are stable in the Einstein-Hilbert sense, which have long been lacking in the positive scalar curvature setting
Killing and conformal Killing tensors
Full text linkThis thesis describes the prolongation connection of Killing tensors in terms of Young symmetrizers. The goal is to give an interpretation to sections of the prolongation bundle for Killing tensors on a manifold as generalized curvature tensors on the cone over that manifold. As a result, this method allows to treat the components of the prolongation bundle as a single object with well-understood symmetries. The developed formalism is then explored in three applications. The first result gives an isomorphism between the symmetric algebra of Killing tensors on a manifold of constant curvature and an algebra generated by parallel two-forms on the cone. That provides a geometric proof of the decomposition of Killing tensors on constant curvature manifolds and the Delong-Takeuchi-Thompson formula, previously obtained by Takeuchi and Thompson.
Secondly, this technique, together with some branching rules for holonomy subgroups, yields a new characterization of Sasakian and 3-Sasakian manifolds in terms of Killing tensors satisfying additional curvature conditions. The third application is a new short proof of the result by Dairbekov and Sharafutdinov that the codimension of the zero set of a non-trivial, trace free, conformal Killing tensor is at least two.
Throughout this work, special emphasis is placed on the representation theory of the appearing tensor bundles. Therefore, the Killing- and conformal Killing operators are introduced as Stein-Weiss operators. Since Young symmetrizers are a well-established tool in describing tensor representations this approach fits perfectly with the goals of the thesis. A natural consequence of this choice are new, geometric proofs of some established results. Besides those mentioned above these cover: (1) A Weitzenböck formula, which implies that all trace free, conformal Killing tensors on manifolds with non-positive sectional curvature are parallel. (2) The decomposition of occurring representations with respect to the reduced holonomy of a Riemannian product yields that the space of trace free, conformal Killing two-tensors on the product is generated by pullbacks of Killing one- and two-tensors on the factors.
Furthermore, this thesis recasts the known examples of Killing tensors on compact Riemannian manifolds in the modern and coordinate free language of differential geometry. It is shown how the example found by Page and Pope generalizes to a construction on all Riemannian submersions with totally geodesic fibres. This technique provides non-parallel symmetric Killing two-tensors on compact Kähler manifolds. That contrasts the fact that on such n-dimensional manifolds do not exist non-parallel Killing forms of degree other than one or n-1. Furthermore, this construction gives a method to compute some eigenvalues of the Lichnerowicz-Laplace operator acting on symmetric two-tensors
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
Horizontal Dirac Operators in CR Geometry
Full text linkIn dieser Dissertation beschäftigen wir uns mit angepassten Zusammenhängen und ihren (horizontalen) Dirac-Operatoren auf strikt pseudokonvexen CR-Mannigfaltigkeiten. Einen Zusammenhang nennen wir dann angepasst, wenn er die relevanten Daten parallelisiert. Wir beschreiben den Raum der angepassten Zusammenhänge, indem wir ihre Torsionstensoren studieren, von denen gewisse Teile durch die Geometrie der Mannigfaltigkeit festgelegt sind, während andere frei wählbar sind. Als Anwendung betrachten wir die Eigenschaften der Dirac-Operatoren, die zu diesen Zusammenhängen gehören.
Weiter betrachten wir horizontale Dirac-Operatoren, die nur in Richtung des horizontalen Bündels H ableiten. Diese Operatoren sind besser an die Sub-Riemannsche Struktur einer CR-Mannigfaltigkeit angepasst als die vollen Dirac-Operatoren. Wir diskutieren, wann diese Operatoren formal selbstadjungiert sind und beweisen eine Weitzenböck-Typ-Formel. Wir konzentrieren uns dann auf den horizontalen Dirac-Operator zum Tanaka-Webster-Zusammenhang. Dieser ändert sich konform kovariant, wenn wir die Kontaktform konform ändern. Für diesen Operator betrachten wir weiterhin zwei Beispiele: Wir betrachten S^1-Bündel über Kähler-Mannigfaltigkeiten, insbesondere berechnen wir für Sphären einen Teil des Spektrums. Außerdem betrachten wir kompakte Quotienten der Heisenberggruppe und berechnen hier in den Dimensionen 3 und 5 das volle Spektrum.
Die horizontalen Dirac-Operatoren sind nicht mehr elliptisch, sondern „elliptisch in Richtung von H“. Mithilfe des Heisenbergkalküls stellen wir fest, dass die horizontalen Dirac-Operatoren nicht hypoelliptisch sind. Im Fall des Tanaka-Webster-Zusammenhangs lässt sich aber zeigen, dass der zugehörige Operator auf gewissen Teilen des Spinorbündels hypoelliptisch ist. Dies genügt, um zu beweisen, dass er (nun auf dem gesamten Spinorbündel) ein reines Punktspektrum hat und die Eigenräume, bis auf den Kern, endlich-dimensional sind und aus glatten Eigenspinoren bestehen.In the present thesis, we study adapted connections and their (horizontal) Dirac operators on strictly pseudoconvex CR manifolds. An adapted connection is one that parallelises the relevant data. We describe the space of adapted connections through their torsion tensors, certain parts of which are determined by the geometry of the manifold, while others may be freely chosen. As an application, we study the properties of the Dirac operators induced by these connections.
We further consider horizontal Dirac operators, which only derive in the direction of the horizontal bundle H. These operators are more adapted to the essentially sub-Riemannian structure of a CR manifold than the full Dirac operators. We discuss the question of their self-adjointness and prove a Weitzenböck type formula for these operators. Focusing on the horizontal Dirac operator associated with the Tanaka-Webster connection, we show that this operator changes in a covariant way if we change the contact form conformally. Moreover, for this operator we discuss two examples: On S^1-bundles over Kähler manifolds, we can compute part of the spectrum and for compact quotients of the Heisenberg group, we determine the whole spectrum in dimensions three and five.
The horizontal Dirac operators are not elliptic, but rather "elliptic in some directions". We review the Heisenberg Calculus for such operators and find that in general, the horizontal Dirac operators are not hypoelliptic. However, in the case of the Tanaka-Webster connection, the associated horizontal Dirac operator is hypoelliptic on certain parts of the spinor bundle and this is enough to prove that its spectrum consists only of eigenvalues and except for the kernel, the corresponding eigenspaces are finite-dimensional spaces of smooth sections
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Mini-Workshop: Quaternion Kähler Structures in Riemannian and Algebraic Geometry
Full text linkMetrics of special holonomy are of central interest in both Riemannian and complex algebraic geometry. We focus on an important classification problem of a particular type of special holonomy manifolds, namely compact quaternion-Kähler with positive scalar curvature (Salamon-LeBrun conjecture). In the language of algebraic geometry this corresponds to the classification of Fano contact manifolds. By bringing together leading experts in both fields this workshop pursued a two-fold goal: First, to revise old and to develop new strategies for proving the most central conjecture in the field of quaternionic Kähler geometry. Second, to introduce young researchers at PhD/PostDoc level to this interdisciplinary circle of ideas
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
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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