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Relevant bibliographies by topics / Generalised flag manifolds

Academic literature on the topic 'Generalised flag manifolds'

Author: Grafiati

Published: 10 March 2023

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Journal articles on the topic "Generalised flag manifolds"

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Alves, Luciana Aparecida, and Neiton Pereira da Silva. "Invariant Einstein metrics on generalized flag manifolds of $Sp(n)$ and $SO(2n)$." Boletim da Sociedade Paranaense de Matemática 38, no. 1 (February 19, 2018): 227. http://dx.doi.org/10.5269/bspm.v38i1.36604.

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It is well known that the Einstein equation on a Riemannian flag manifold $(G/K,g)$ reduces to an algebraic system if $g$ is a $G$-invariant metric. In this paper we obtain explicitly new invariant Einstein metrics on generalized flag manifolds of $Sp(n)$ and $SO(2n)$; and we compute the Einstein system for generalized flag manifolds of type $Sp(n)$. We also consider the isometric problem for these Einstein metrics.

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Yadav, S., and D. L. Suthar. "On Kenmatsu manifolds Satisfying Certain Conditions." Journal of the Tensor Society 3, no. 00 (June 30, 2009): 19–26. http://dx.doi.org/10.56424/jts.v3i01.9968.

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In this paper, we study 3-dimensional Kenmostu manifolds, weakely Ricci symmetric Kenmostu manifolds and generalized Ricci recurrent Kenmostu manifolds and prove that conformably flat Kenmostu manifold is -Einstein manifolds, deduced that the square length of Ricci tensor. Further proved that if weakly Ricci-symmetric Kenmostu manifolds satisfies Ricci symmetric condition then manifolds Einstein manifold. In last we prove that if generalized Ricci recurrent Kenmostu manifolds satisfies the condition ( )(Y)=0 then .

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ARVANITOYEORGOS, ANDREAS, IOANNIS CHRYSIKOS, and YUSUKE SAKANE. "HOMOGENEOUS EINSTEIN METRICS ON GENERALIZED FLAG MANIFOLDS WITH FIVE ISOTROPY SUMMANDS." International Journal of Mathematics 24, no. 10 (September 2013): 1350077. http://dx.doi.org/10.1142/s0129167x13500778.

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We construct the homogeneous Einstein equation for generalized flag manifolds G/K of a compact simple Lie group G whose isotropy representation decomposes into five inequivalent irreducible Ad (K)-submodules. To this end, we apply a new technique which is based on a fibration of a flag manifold over another such space and the theory of Riemannian submersions. We classify all generalized flag manifolds with five isotropy summands, and we use Gröbner bases to study the corresponding polynomial systems for the Einstein equation. For the generalized flag manifolds E6/(SU(4) × SU(2) × U(1) × U(1)) and E7/(U(1) × U(6)) we find explicitly all invariant Einstein metrics up to isometry. For the generalized flag manifolds SO (2ℓ + 1)/( U (1) × U (p) × SO (2(ℓ - p - 1) + 1)) and SO (2ℓ)/( U (1) × U (p) × SO (2(ℓ - p - 1))) we prove existence of at least two non-Kähler–Einstein metrics. For small values of ℓ and p we give the precise number of invariant Einstein metrics.

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De, Uday Chand, Abdallah Abdelhameed Syied, Nasser Bin Turki, and Suliman Alsaeed. "A Study of Generalized Projective P − Curvature Tensor on Warped Product Manifolds." Journal of Mathematics 2021 (December 27, 2021): 1–10. http://dx.doi.org/10.1155/2021/7882356.

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The main aim of this study is to investigate the effects of the P − curvature flatness, P − divergence-free characteristic, and P − symmetry of a warped product manifold on its base and fiber (factor) manifolds. It is proved that the base and the fiber manifolds of the P − curvature flat warped manifold are Einstein manifold. Besides that, the forms of the P − curvature tensor on the base and the fiber manifolds are obtained. The warped product manifold with P − divergence-free characteristic is investigated, and amongst many results, it is proved that the factor manifolds are of constant scalar curvature. Finally, P − symmetric warped product manifold is considered.

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Haseeb, Abdul, and Rajendra Prasad. "Certain results on Lorentzian para-Kenmotsu manifolds." Boletim da Sociedade Paranaense de Matemática 39, no. 3 (January 1, 2021): 201–20. http://dx.doi.org/10.5269/bspm.40607.

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The object of the present paper is to study Lorentzian para-Kenmotsu manifolds with respect to the quarter-symmetric metric connection. First we study Lorentzian para-Kenmotsu manifolds with respect to the quarter-symmetric metric connection satisfying the conditions $\bar R\cdot \bar S=0$ and $\bar S\cdot \bar R=0$. After that we study $\phi$-conformally flat, $\phi$-conharmonically flat, $\phi$-concircularly flat, $\phi$-projectively flat and conformally flat Lorentzian para-Kenmotsu manifolds with respect to the quarter-symmetric metric connection and it is shown that in each of these case the manifold is generalized $\eta$-Einstein manifold.

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Shenawy, Sameh, and Bülent Ünal. "The W2-curvature tensor on warped product manifolds and applications." International Journal of Geometric Methods in Modern Physics 13, no. 07 (July 25, 2016): 1650099. http://dx.doi.org/10.1142/s0219887816500997.

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The purpose of this paper is to study the [Formula: see text]-curvature tensor on (singly) warped product manifolds as well as on generalized Robertson–Walker and standard static space-times. Some different expressions of the [Formula: see text]-curvature tensor on a warped product manifold in terms of its relation with [Formula: see text]-curvature tensor on the base and fiber manifolds are obtained. Furthermore, we investigate [Formula: see text]-curvature flat warped product manifolds. Many interesting results describing the geometry of the base and fiber manifolds of a [Formula: see text]-curvature flat warped product manifold are derived. Finally, we study the [Formula: see text]-curvature tensor on generalized Robertson–Walker and standard static space-times; we explore the geometry of the fiber of these warped product space-time models that are [Formula: see text]-curvature flat.

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ARVANITOYEORGOS, ANDREAS, and IOANNIS CHRYSIKOS. "INVARIANT EINSTEIN METRICS ON GENERALIZED FLAG MANIFOLDS WITH TWO ISOTROPY SUMMANDS." Journal of the Australian Mathematical Society 90, no. 2 (April 2011): 237–51. http://dx.doi.org/10.1017/s1446788711001303.

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AbstractLet M=G/K be a generalized flag manifold, that is, an adjoint orbit of a compact, connected and semisimple Lie group G. We use a variational approach to find non-Kähler homogeneous Einstein metrics for flag manifolds with two isotropy summands. We also determine the nature of these Einstein metrics as critical points of the scalar curvature functional under fixed volume.

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Nagaraja, H. G., and C. R. Premalatha. "Da-Homothetic Deformation of K-Contact Manifolds." ISRN Geometry 2013 (December 16, 2013): 1–7. http://dx.doi.org/10.1155/2013/392608.

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We study Da-homothetic deformations of K-contact manifolds. We prove that Da-homothetically deformed K-contact manifold is a generalized Sasakian space form if it is conharmonically flat. Further, we find expressions for scalar curvature of Da-homothetically deformed K-contact manifolds.

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RANDJBAR-DAEMI, S., and J. STRATHDEE. "THE RENORMAUZATION GROUP FOR FLAG MANIFOLDS." International Journal of Modern Physics A 08, no. 20 (August 10, 1993): 3509–28. http://dx.doi.org/10.1142/s0217751x93001417.

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The renormalization group equations for a class of nonrelativistic quantum σ-models targeted on flag manifolds are given. These models emerge in a continuum limit of generalized Heisenberg antiferromagnets. The case of the [Formula: see text] manifold is studied in greater detail. We show that at zero temperature there is a fixed point of the RG transformations in (2 + ε) dimensions where the theory becomes relativistic. We study the linearized RG transformations in the vicinity of this fixed point and show that half of the couplings are irrelevant. We also show that at this fixed point there is an enlargement of the global isometries of the target manifold. We construct a discrete non-Abelian enlargement of this kind.

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Zhuang, Xiaobo. "Vanishing theorems of generalized Witten genus for generalized complete intersections in flag manifolds." International Journal of Mathematics 27, no. 09 (August 2016): 1650076. http://dx.doi.org/10.1142/s0129167x16500762.

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We propose a potential function [Formula: see text] for the cohomology ring of partial flag manifolds. We prove a formula expressing integrals over partial flag manifolds by residues, which generalizes [E. Witten, The Verlinde algebra and the cohomology of the Grassmannian, in Geometry, Topology, Physics (International Press, 1995), pp. 357–422]. Using this formula, we prove a Landweber–Stong type vanishing theorem for generalized [Formula: see text] complete intersections in flag manifolds, which serves as evidence for the [Formula: see text] version of Stolz conjecture [Q. Chen, F. Han and W. Zhang, Generalized Witten genus and vanishing theorems, J. Differential Geom. 88(1) (2011) 1–39].

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More sources

Dissertations / Theses on the topic "Generalised flag manifolds"

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Treib, Nicolaus [Verfasser], and Anna [Akademischer Betreuer] Wienhard. "Generalized Schottky groups, oriented flag manifolds and proper actions / Nicolaus Treib ; Betreuer: Anna Wienhard." Heidelberg : Universitätsbibliothek Heidelberg, 2018. http://d-nb.info/1177149311/34.

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Friday, Brian Matthew. "VANISHING LOCAL SCALAR INVARIANTS ON GENERALIZED PLANE WAVE MANIFOLDS." CSUSB ScholarWorks, 2019. https://scholarworks.lib.csusb.edu/etd/884.

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Characterizing a manifold up to isometry is a challenging task. A manifold is a topological space. One may equip a manifold with a metric, and generally speaking, this metric determines how the manifold “looks". An example of this would be the unit sphere in R3. While we typically envision the standard metric on this sphere to give it its familiar shape, one could define a different metric on this set of points, distorting distances within this set to make it seem perhaps more ellipsoidal, something not isometric to the standard round sphere. In an effort to distinguish manifolds up to isometry, we wish to compute meaningful invariants. For example, the Riemann curvature tensor and its surrogates are examples of invariants one could construct. Since these objects are generally too complicated to compare and are not real valued, we construct scalar invariants from these objects instead. This thesis will explore these invariants and exhibit a special family of manifolds that are not flat on which all of these invariants vanish. We will go on to properly define, and gives examples of, manifolds, metrics, tangent vector fields, and connections. We will show how to compute the Christoffel symbols that define the Levi-Civita connection, how to compute curvature, and how to raise and lower indices so that we can produce scalar invariants. In order to construct the curvature operator and curvature tensor, we use the miracle of pseudo-Riemannian geometry, i.e., the Levi-Civita connection, the unique torsion free and metric compatible connection on a manifold. Finally, we examine Generalized Plane Wave Manifolds, and show that all scalar invariants of Weyl type on these manifolds vanish, despite the fact that many of these manifolds are not flat.

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LOHOVE, SIMON PETER. "Holomorphic curvature of Kähler Einstein metrics on generalised flag manifolds." Doctoral thesis, 2019. http://hdl.handle.net/2158/1151431.

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We analyse the holomorphic curvature of Kähler metrics on generalised flag manifolds with respect to the question of strict positivity. The main results are twofold: Firstly, we show that most generalised flag manifolds with second betti number smaller than 3 have positive holomorphic curvature for any Kähler metric. Secondly, using fairly different techniques we obtain that every generalised flag manifold of rank four or less has positive holomorphic curvature with respect to the Kähler-Einstein metric.

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Χρυσικός, Ιωάννης. "Ομογενείς μετρικές Einstein σε γενικευμένες πολλαπλότητες σημαιών." Thesis, 2011. http://nemertes.lis.upatras.gr/jspui/handle/10889/4418.

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Μια πολλαπλότητα Riemann (M, g) ονομάζεται Einstein αν έχει σταθερή καμπυλότητα Ricci. Είναι γνωστό ότι αν (M=G/K, g) είναι μια συμπαγής ομογενής πολλαπλότητα Riemann, τότε οι G-αναλλοίωτες μετρικές Einstein μοναδιαίου όγκου, είναι τα κρίσιμα σημεία του συναρτησοειδούς ολικής βαθμωτής καμπυλότητας περιορισμένο στο χώρο των G-αναλλοίωτων μετρικών με όγκο 1. Για μια G-αναλλοίωτη μετρική Riemann η εξίσωση Einstein ανάγεται σε ένα σύστημα αλγεβρικών εξισώσεων. Οι θετικές πραγματικές λύσεις του συστήματος αυτού είναι ακριβώς οι G-αναλλοίωτες μετρικές Einstein που δέχεται η πολλαπλότητα Μ. Μια σημαντική οικογένεια συμπαγών ομογενών χώρων αποτελείται από τις γενικευμένες πολλαπλότητες σημαιών. Κάθε τέτοιος χώρος είναι μια τροχιά της συζυγούς αναπαράστασης μιας συμπαγούς, συνεκτικής, ημι-απλής ομάδας Lie G. Πρόκειται για ομογενείς πολλαπλότητες της μορφής G/C(S), όπου C(S) είναι ο κεντροποιητής ενός δακτυλίου S στην G. Κάθε τέτοιος χώρος δέχεται ένα πεπερασμένο πλήθος από G-αναλλοίωτες μετρικές Kahler-EInstein. Στην παρούσα διατριβή ταξινομούμε όλες τις πολλαπλότητες σημαιών G/K που αντιστοιχούν σε μια απλή ομάδα Lie G, των οποίων η ισοτροπική αναπαράσταση διασπάται σε 2 ή 4 μη αναγώγιμους και μη ισοδύναμους Ad(K)-αναλλοίωτους προσθετέους. Για κάθε τέτοιο χώρο λύνουμε την αναλλοίωτη εξίσωση Εinstein, και παρουσιάζουμε την αναλυτική μορφή νέων G-αναλλοίωτων μετρικών Einstein. Στις περισσότερες περιπτώσεις παρουσιάζουμε την πλήρη ταξινόμηση των αναλλοίωτων μετρικών Einstein. Επίσης εξετάζουμε το ισομετρικό πρόβλημα. Για την κατασκευή της εξίσωσης Einstein σε κάποιες πολλαπλότητες σημαιών με 4 ισοτροπικούς προσθετέους χρησιμοποιούμε την νηματοποίηση συστροφής που δέχεται κάθε πολλαπλότητα σημαιών επί ενός ισοτροπικά μη αναγώγιμου συμμετρικού χώρου συμπαγούς τύπου. Αυτή η μέθοδος είναι καινούργια και μπορεί να εφαρμοστεί και σε άλλες πολλαπλότητες σημαιών.
A Riemannian manifold (M, g) is called Einstein, if it has constant Ricci curvature. It is well known that if (M=G/K, g) is a compact homogeneous Riemannian manifold, then the G-invariant \tl{Einstein} metrics of unit volume, are the critical points of the scalar curvature function restricted to the space of all G-invariant metrics with volume 1. For a G-invariant Riemannian metric the Einstein equation reduces to a system of algebraic equations. The positive real solutions of this system are the $G$-invariant Einstein metrics on M. An important family of compact homogeneous spaces consists of the generalized flag manifolds. These are adjoint orbits of a compact semisimple Lie group. Flag manifolds of a compact connected semisimple Lie group exhaust all compact and simply connected homogeneous Kahler manifolds and are of the form G/C(S), where C(S) is the centralizer (in G) of a torus S in G. Such homogeneous spaces admit a finite number of G-invariant complex structures, and for any such complex structure there is a unique compatible G-invariant Kahler-Einstein metric. In this thesis we classify all flag manifolds M=G/K of a compact simple Lie group G, whose isotropy representation decomposes into 2 or 4, isotropy summands. For these spaces we solve the (homogeneous) Einstein equation, and we obtain the explicit form of new G-invariant Einstein metrics. For most cases we give the classification of homogeneous Einstein metrics. We also examine the isometric problem. For the construction of the Einstein equation on certain flag manifolds with four isotropy summands, we apply for first time the twistor fibration of a flag manifold over an isotropy irreducible symmetric space of compact type. This method is new and it can be used also for other flag manifolds. For flag manifolds with two isotropy summands, we use the restricted Hessian and we characterize the new Einstein metrics as local minimum points of the scalar curvature function restricted to the space of G-invariant Riemannian metrics of volume 1. We mention that the classification of flag manifolds with two isotropy summands gives us new examples of homogeneous spaces, for which the motion of a charged particle under the electromagnetic field, and the geodesics curves, are completely determined.

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Books on the topic "Generalised flag manifolds"

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Ortaçgil, Ercüment H. Klein Geometries. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198821656.003.0017.

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Up to now, the discussion has been mainly concerned with Lie groups and their curved analogs, namely, parallelizable manifolds and their curvatures. The problem is to generalize this construction to arbitrary geometric structures. The first step is to study the flat case, and this is the subject of this chapter.

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Book chapters on the topic "Generalised flag manifolds"

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Arvanitoyeorgos, Andreas. "Generalized flag manifolds." In The Student Mathematical Library, 95–112. Providence, Rhode Island: American Mathematical Society, 2003. http://dx.doi.org/10.1090/stml/022/07.

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Zinn-Justin, Jean. "Generalized non-linear σ-models in two dimensions." In Quantum Field Theory and Critical Phenomena, 692–720. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198834625.003.0029.

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This chapter describes the formal properties, and discusses the renormalization, of quantum field theories (QFT) based on homogeneous spaces: coset spaces of the form G/H, where G is a compact Lie group and H a Lie subgroup. In physics, they appear naturally in the case of spontaneous symmetry breaking, and describe the interaction between Goldstone modes. Homogeneous spaces are associated with non-linear realizations of group representations. There exist natural ways to embed these manifolds in flat Euclidean spaces, spaces in which the symmetry group acts linearly. As in the example of the non-linear σ-model, this embedding is first used, because the renormalization properties are simpler, and the physical interpretation of the more direct correlation functions. Then, in a generic parametrization, the renormalization problem is solved by the introduction of a Becchi–Rouet–Stora–Tyutin (BRST)-like symmetry with anticommuting (Grassmann) parameters, which also plays an essential role in quantized gauge theories. The more specific properties of models corresponding to a special class of homogeneous spaces, symmetric spaces (like the non-linear σ-model), are studied. These models are characterized by the uniqueness of the metric and thus, of the classical action. In two dimensions, from the classical field equations an infinite number of non-local conservation laws can be derived. The field and the unique coupling renormalization group (RG) functions are calculated at one-loop order, in two dimensions, and shown to imply asymptotic freedom.

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Conference papers on the topic "Generalised flag manifolds"

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ARVANITOYEORGOS, Andreas, Ioannis CHRYSIKOS, and Yusuke SAKANE. "HOMOGENEOUS EINSTEIN METRICS ON GENERALIZED FLAG MANIFOLDS WITH G2-TYPE 𝔱-ROOTS." In Proceedings of the 3rd International Colloquium on Differential Geometry and Its Related Fields. WORLD SCIENTIFIC, 2013. http://dx.doi.org/10.1142/9789814541817_0002.

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Nishimori, Yasunori, Shotaro Akaho, and Mark D. Plumbley. "Riemannian Optimization Method on Generalized Flag Manifolds for Complex and Subspace ICA." In Bayesian Inference and Maximum Entropy Methods In Science and Engineering. AIP, 2006. http://dx.doi.org/10.1063/1.2423264.

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ARVANITOYEORGOS, Andreas, Ioannis CHRYSIKOS, and Yusuke SAKANE. "HOMOGENEOUS EINSTEIN METRICS ON GENERALIZED FLAG MANIFOLDS Sp(n)/(U(p) × U(q) × Sp(n-p-q))." In Proceedings of the 2nd International Colloquium on Differential Geometry and Its Related Fields. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814355476_0001.

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