Relevant bibliographies by topics / Cohomogeneity

Academic literature on the topic 'Cohomogeneity'

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Published: 10 March 2023

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Journal articles on the topic "Cohomogeneity"

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DANCER, ANDREW, and ANDREW SWANN. "QUATERNIONIC KAHLER MANIFOLDS OF COHOMOGENEITY ONE." International Journal of Mathematics 10, no. 05 (August 1999): 541–70. http://dx.doi.org/10.1142/s0129167x99000215.

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Classification results are given for (i) compact quaternionic Kähler manifolds with a cohomogeneity-one action of a semi-simple group, (ii) certain complete hyperKähler manifolds with a cohomogeneity-two action of a semi-simple group preserving each complex structure, (iii) compact 3-Sasakian manifolds which are cohomogeneity one with respect to a group of 3-Sasakian symmetries. Information is also obtained about non-compact quaternionic Kähler manifolds of cohomogeneity one and the cohomogeneity of adjoint orbits in complex semi-simple Lie algebras.
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Deng, Shaoqiang, and Jifu Li. "Some cohomogeneity one Einstein–Randers metrics on 4-manifolds." International Journal of Geometric Methods in Modern Physics 14, no. 03 (February 14, 2017): 1750044. http://dx.doi.org/10.1142/s021988781750044x.

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The Page metric on [Formula: see text] is a cohomogeneity one Einstein–Riemannian metric, and is the only known cohomogeneity one Einstein–Riemannian metric on compact [Formula: see text]-manifolds. It has been a long standing problem whether there exists another cohomogeneity one Einstein–Riemannian metric on [Formula: see text]-manifolds. In this paper, we construct some examples of cohomogeneity one Einstein–Randers metrics on simply connected 4-manifolds. This shows that, although cohomogeneity one Einstein–Riemmian 4-manifolds are rare, non-Riemannian examples may exist at large.
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Li, Jifu, Zhiguang Hu, and Shaoqiang Deng. "Cohomogeneity One Randers Metrics." Canadian Mathematical Bulletin 59, no. 3 (September 1, 2016): 575–84. http://dx.doi.org/10.4153/cmb-2015-009-5.

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AbstractAn action of a Lie group G on a smooth manifold M is called cohomogeneity one if the orbit space M/G is of dimension 1. A Finsler metric F on M is called invariant if F is invariant under the action of G. In this paper, we study invariant Randers metrics on cohomogeneity one manifolds. We first give a sufficient and necessary condition for the existence of invariant Randers metrics on cohomogeneity one manifolds. Then we obtain some results on invariant Killing vector fields on the cohomogeneity one manifolds and use them to deduce some sufficient and necessary conditions for a cohomogeneity one Randers metric to be Einstein.
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Galaz-García, Fernando, and Masoumeh Zarei. "Cohomogeneity one Alexandrov spaces in low dimensions." Annals of Global Analysis and Geometry 58, no. 2 (July 7, 2020): 109–46. http://dx.doi.org/10.1007/s10455-020-09716-7.

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Abstract Alexandrov spaces are complete length spaces with a lower curvature bound in the triangle comparison sense. When they are equipped with an effective isometric action of a compact Lie group with one-dimensional orbit space, they are said to be of cohomogeneity one. Well-known examples include cohomogeneity-one Riemannian manifolds with a uniform lower sectional curvature bound; such spaces are of interest in the context of non-negative and positive sectional curvature. In the present article we classify closed, simply connected cohomogeneity-one Alexandrov spaces in dimensions 5, 6 and 7. This yields, in combination with previous results for manifolds and Alexandrov spaces, a complete classification of closed, simply connected cohomogeneity-one Alexandrov spaces in dimensions at most 7.
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Julio-Batalla, Jurgen, and Jimmy Petean. "Nodal solutions of Yamabe-type equations on positive Ricci curvature manifolds." Proceedings of the American Mathematical Society 149, no. 10 (July 23, 2021): 4419–29. http://dx.doi.org/10.1090/proc/15548.

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We consider a closed cohomogeneity one Riemannian manifold ( M n , g ) (M^n,g) of dimension n ≥ 3 n\geq 3 . If the Ricci curvature of M M is positive, we prove the existence of infinite nodal solutions for equations of the form − Δ g u + λ u = λ u q -\Delta _g u + \lambda u = \lambda u^q with λ > 0 \lambda >0 , q > 1 q>1 . In particular for a positive Einstein manifold which is of cohomogeneity one or fibers over a cohomogeneity one Einstein manifold we prove the existence of infinite nodal solutions for the Yamabe equation, with a prescribed number of connected components of its nodal domain.
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Díaz-Ramos, José Carlos, Miguel Domínguez-Vázquez, and Alberto Rodríguez-Vázquez. "Homogeneous and inhomogeneous isoparametric hypersurfaces in rank one symmetric spaces." Journal für die reine und angewandte Mathematik (Crelles Journal) 2021, no. 779 (August 17, 2021): 189–222. http://dx.doi.org/10.1515/crelle-2021-0043.

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Abstract We conclude the classification of cohomogeneity one actions on symmetric spaces of rank one by classifying cohomogeneity one actions on quaternionic hyperbolic spaces up to orbit equivalence. As a by-product of our proof, we produce uncountably many examples of inhomogeneous isoparametric families of hypersurfaces with constant principal curvatures in quaternionic hyperbolic spaces.
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Cleyton, Richard, and Andrew Swann. "Cohomogeneity-one G2-structures." Journal of Geometry and Physics 44, no. 2-3 (December 2002): 202–20. http://dx.doi.org/10.1016/s0393-0440(02)00074-8.

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Galaz-Garcia, Fernando, and Catherine Searle. "Cohomogeneity one Alexandrov spaces." Transformation Groups 16, no. 1 (February 16, 2011): 91–107. http://dx.doi.org/10.1007/s00031-011-9122-0.

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AHMADI, P., and S. M. B. KASHANI. "Cohomogeneity one Minkowski space Rn1." Publicationes Mathematicae Debrecen 78, no. 1 (January 1, 2011): 49–59. http://dx.doi.org/10.5486/pmd.2011.4392.

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Dancer, Andrew, and Andrew Swann. "Hyperkähler metrics of cohomogeneity one." Journal of Geometry and Physics 21, no. 3 (February 1997): 218–30. http://dx.doi.org/10.1016/s0393-0440(96)00017-4.

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Dissertations / Theses on the topic "Cohomogeneity"

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Betancourt, de la Parra Alejandro. "Cohomogeneity one Ricci solitons." Thesis, University of Oxford, 2016. https://ora.ox.ac.uk/objects/uuid:8f924daf-d6e6-4150-96c2-d156a6a7815a.

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In this work we study the cohomogeneity one Ricci soliton equation viewed as a dynamical system. We are particularly interested in the relation between integrability of the associated system and the existence of explicit, closed form solutions of the soliton equation. The contents are organized as follows. The first chapter is an introduction to Ricci ow and Ricci solitons and their basic properties. We reformulate the rotationally symmetric Ricci soliton equation on Rn+1 as a system of ODE's following the treatment in [14]. In Chapter 2 we carry out a Painlevé analysis of the previous system. For the steady case, dimensions where n is a perfect square are singled out. The cases n = 4, 9 are particularly distinguished. In the expanding case, only dimension n = 1 is singled out. In Chapter 3 we reformulate the cohomogeneity one Ricci soliton equation as a Hamiltonian system with constraint. We obtain a conserved quantity for this system and produce explicit formulas for solitons of dimension 5. In Chapter 4 we introduce the notion of superpotential and use it to produce more explicit formulas for solitons of steady, expanding and shrinking type. In Chapter 5 we carry out a Painlevé anaylsis of the Hamiltonian corresponding to solitons over warped products of Einstein manifolds with positive scalar curvature. This analysis singles out the cases discussed in the previous chapters. We also carry out an analysis of the Hamiltonian corresponding to the Bérard Bergery ansatz [5]. This analysis singles out a 1-parameter family of solutions.
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Kudzin, Matthew. "Cohomogeneity one manifolds of non-negative curvature." [Bloomington, Ind.] : Indiana University, 2004. http://wwwlib.umi.com/dissertations/fullcit/3162245.

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Thesis (Ph.D.)--Indiana University, Dept. of Mathematics, 2004.
Title from PDF t.p. (viewed Dec. 1, 2008). Source: Dissertation Abstracts International, Volume: 66-01, Section: B, page: 0307. Chair: Ji-Ping Sha.
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Chiru, Eduard. "Harmonic 2-forms on cohomogeneity one 4-manifolds." [Bloomington, Ind.] : Indiana University, 2005. http://wwwlib.umi.com/dissertations/fullcit/3204303.

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Thesis (Ph.D.)--Indiana University, Dept. of Mathematics, 2005.
Source: Dissertation Abstracts International, Volume: 67-01, Section: B, page: 0300. Adviser: Ji-Ping Sha. "Title from dissertation home page (viewed Feb. 21, 2007)."
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Hassani, Masoud. "Study of cohomogeneity one three dimensional Einstein universe." Thesis, Avignon, 2018. http://www.theses.fr/2018AVIG0421/document.

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Dans cette thèse des actions conformes de cohomogénéité un sur l'univers d'Einstein tridimensionel sont classifiées. Notre stratégie est d'établir dans un premier temps quel peut être le groupe de transformations conformes impliqué, à conjugaison près. Nous décrivons aussi la topologie et la nature causale des orbites d'une telle action
In this thesis, the conformal actions of cohomogeneity one on the three-dimensional Einstein universe are classified. Our strategy in this study is to determine the representation of the acting group in the group of conformal transformations of Einstein universe up to conjugacy. Also, we describe the topology and the causal character of the orbits induced by cohomogeneity one actions in Einstein universe
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Frank, Philipp [Verfasser], and Burkhard [Akademischer Betreuer] Wilking. "Cohomogeneity one manifolds with positive Euler characteristic / Philipp Frank. Betreuer: Burkhard Wilking." Münster : Universitäts- und Landesbibliothek der Westfälischen Wilhelms-Universität, 2011. http://d-nb.info/1027017088/34.

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Grieger, Elisabeth Sarah Francis. "On heat kernel methods and curvature asymptotics for certain cohomogeneity one Riemannian manifolds." Thesis, King's College London (University of London), 2016. http://kclpure.kcl.ac.uk/portal/en/theses/on-heat-kernel-methods-and-curvature-asymptotics-for-certain-cohomogeneity-one-riemannian-manifolds(40d2e3ab-3eb8-4141-bcc5-ca38e0705f65).html.

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We study problems related to the metric of a Riemannian manifold with a particular focus on certain cohomogeneity one metrics. In Chapter 2 we study a set of cohomogeneity one Einstein metrics found by A. Dancer and M. Wang. We express these in terms of elementary functions and nd explicit sectional curvature formulae which are then used to determine sectional curvature asymptotics of the metrics. In Chapter 3 we construct a non-standard parametrix for the heat kernel on a product manifold with multiply warped Riemannian metric. The special feature of this parametrix is that it separates the contribution of the warping functions and the heat data on the factors; this cannot be achieved via the standard approach. In Chapter 4 we determine explicit formulae for the resolvent symbols associated with the Laplace Beltrami operator over a closed Riemannian manifold and apply these to motivate an alternative method for computing heat trace coecients. This method is entirely based on local computations and to illustrate this we recover geometric formulae for the heat coecients. Furthermore one can derive topological identities via this approach; to demonstrate this application we nd explicit formulae for the resolvent symbols associated with Laplace operators on a Riemann surface and recover the Riemann-Roch formula. In the nal chapter we report on an area of current research: we introduce a class of symbols for pseudodi erential operators on simple warped products which is closed under composition. We then extend the canonical trace to this setting, using a cut - o integral, and nd an explicit formula for the extension in terms of integrals over the factor.
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Buzano, Maria. "Topics in Ricci flow with symmetry." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:36df458b-b7cc-4447-a979-6adb24ff7959.

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In this thesis, we study the Ricci flow and Ricci soliton equations on Riemannian manifolds which admit a certain degree of symmetry. More precisely, we investigate the Ricci soliton equation on connected Riemannian manifolds, which carry a cohomogeneity one action by a compact Lie group of isometries, and the Ricci flow equation for invariant metrics on a certain class of compact and connected homogeneous spaces. In the first case, we prove that the initial value problem for a cohomogeneity one gradient Ricci soliton around a singular orbit of the group action always has a solution, under a technical assumption. However, this solution is in general not unique. This is a generalisation of the analogous result for the Einstein equation, which was proved by Eschenburg and Wang in their paper "Initial value problem for cohomogeneity one Einstein metrics". In the second case, by studying the corresponding system of nonlinear ODEs, we identify a class of singular behaviours for the homogeneous Ricci flow on these spaces. The singular behaviours that we find all correspond to type I singularities, which are modelled on rigid shrinking solitons. In the case where the isotropy representation decomposes into two invariant irreducible inequivalent summands, we also investigate the existence of ancient solutions and relate this to the existence and non existence of invariant Einstein metrics. Furthermore, in this special case, we also allow the initial metric to be pseudo- Riemannian and we investigate the existence of immortal solutions. Finally, we study the behaviour of the scalar curvature for this more general situation and show that in the Riemannian case it always has to turn positive in finite time, if it was negative initially. By contrast, in the pseudo-Riemannian case, there are certain initial conditions which preserve negativity of the scalar curvature.
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Reidegeld, Frank [Verfasser]. "Spin(7)-manifolds of cohomogeneity one / vorgelegt von Frank Reidegeld." 2008. http://d-nb.info/99762549X/34.

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Panelli, Francesco. "Representations admitting a toric reduction." Doctoral thesis, 2018. http://hdl.handle.net/2158/1118268.

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We study representations (G,V), where G is a compact and connected Lie group acting by isometries on the finite dimensional real euclidean vector space V, such that the orbit space V/G is isometric to the orbit spave W/H of a representation (H,W) where H is a finite extension of a torus. In particular we classify such representations (G,V) when G is simple.
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Books on the topic "Cohomogeneity"

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Compact connected lie transformation groups on spheres with low cohomogeneity, I. Providence, R.I: American Mathematical Society, 1996.

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Straume, Eldar. Compact connected Lie transformation groups on spheres with low cohomogeneity, II. Providence, R.I: American Mathematical Society, 1997.

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Book chapters on the topic "Cohomogeneity"

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Alexandrino, Marcos M., and Renato G. Bettiol. "Low Cohomogeneity Actions and Positive Curvature." In Lie Groups and Geometric Aspects of Isometric Actions, 139–83. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-16613-1_6.

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Ziller, Wolfgang. "On the Geometry of Cohomogeneity One Manifolds with Positive Curvature." In Riemannian Topology and Geometric Structures on Manifolds, 233–62. Boston, MA: Birkhäuser Boston, 2009. http://dx.doi.org/10.1007/978-0-8176-4743-8_10.

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Dancer, Andrews, and Ian A. B. Strachan. "Cohomogeneity-One Kähler Metrics." In twistor theory, 9–28. Routledge, 2017. http://dx.doi.org/10.1201/9780203734889-2.

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Conti, Diego, Thomas Bruun Madsen, and Simon Salamon. "Quaternionic Geometry in Dimension 8." In Geometry and Physics: Volume I, 91–114. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198802013.003.0005.

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This chapter describes the 8-dimensional Wolf spaces as cohomogeneity one SU(3)-manifolds, and discover perturbations of the quaternion-kähler metric on the simply connected 8-manifold G2/SO(4) that carry a closed fundamental 4-form but are not Einstein.
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Tod, K. P. "Cohomogeneity-One Metrics with Self-Dual Weyl Tensor." In twistor theory, 171–84. Routledge, 2017. http://dx.doi.org/10.1201/9780203734889-13.

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Eschenburg, J. H., and Mckenzie Y. Wang. "The ODE System Arising from Cohomogeneity One Einstein Metrics." In Geometry and physics, 157–65. CRC Press, 2021. http://dx.doi.org/10.1201/9781003072393-10.

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Conference papers on the topic "Cohomogeneity"

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Dancer, Andrew, Mckenzie Y. Wang, Carlos Herdeiro, and Roger Picken. "Cohomogeneity one Ricci solitons." In XIX INTERNATIONAL FALL WORKSHOP ON GEOMETRY AND PHYSICS. AIP, 2011. http://dx.doi.org/10.1063/1.3599132.

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KASHANI, S. M. B. "ON COHOMOGENEITY ONE RIEMANNIAN MANIFOLDS." In Proceedings of the Summer School. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812810571_0010.

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Jorge, Rogério, Ednilton S. de Oliveira, and Jorge V. Rocha. "Superradiance of rotating cohomogeneity-1 black holes: Scalar case." In Proceedings of the MG14 Meeting on General Relativity. WORLD SCIENTIFIC, 2017. http://dx.doi.org/10.1142/9789813226609_0187.

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Díaz-Ramos, José Carlos. "THE ORBITS OF COHOMOGENEITY ONE ACTIONS ON COMPLEX HYPERBOLIC SPACES." In Proceedings of the VIII International Colloquium. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789814261173_0014.

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HASHIMOTO, Kaname. "ON THE CONSTRUCTION OF COHOMOGENEITY ONE SPECIAL LAGRANGIAN SUBMANIFOLDS IN THE COTANGENT BUNDLE OF THE SPHERE." In Proceedings of the International Workshop in Honor of S Maeda's 60th Birthday. WORLD SCIENTIFIC, 2013. http://dx.doi.org/10.1142/9789814566285_0013.

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Reports on the topic "Cohomogeneity"

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Mirzaei, Reza. Cohomogeneity Two Riemannian Manifolds of Non-Positive Curvature. GIQ, 2012. http://dx.doi.org/10.7546/giq-13-2012-233-244.

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R. Mirzaie. Topological Properties of Some Cohomogeneity on Riemannian Manifolds of Nonpositive Curvature. GIQ, 2012. http://dx.doi.org/10.7546/giq-3-2002-351-359.

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Abreu, Miguel. Toric Kähler Metrics: Cohomogeneity One Examples of Constant Scalar Curvature in Action- Angle Coordinates. GIQ, 2012. http://dx.doi.org/10.7546/giq-11-2010-11-41.

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Abreu, Miguel. Toric Kähler Metrics: Cohomogeneity One Examples of Constant Scalar Curvature in Action-Angle Coordinates. Journal of Geometry and Symmetry in Physics, 2012. http://dx.doi.org/10.7546/jgsp-17-2010-1-33.

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