Academic literature on the topic 'Riemannian symmetric spaces'
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Journal articles on the topic "Riemannian symmetric spaces":
Jimenez, J. A. "Riemannian 4-Symmetric Spaces." Transactions of the American Mathematical Society 306, no. 2 (April 1988): 715. http://dx.doi.org/10.2307/2000819.
Jim{énez, J. A. "Riemannian $4$-symmetric spaces." Transactions of the American Mathematical Society 306, no. 2 (February 1, 1988): 715. http://dx.doi.org/10.1090/s0002-9947-1988-0933314-6.
Berezovski, Volodymyr, Yevhen Cherevko, and Lenka Rýparová. "Conformal and Geodesic Mappings onto Some Special Spaces." Mathematics 7, no. 8 (July 25, 2019): 664. http://dx.doi.org/10.3390/math7080664.
Burstall, Francis, Simone Gutt, and John Rawnsley. "Twistor spaces for Riemannian symmetric spaces." Mathematische Annalen 295, no. 1 (January 1993): 729–43. http://dx.doi.org/10.1007/bf01444914.
Petrović, Miloš Z., Mića S. Stanković, and Patrik Peška. "On Conformal and Concircular Diffeomorphisms of Eisenhart’s Generalized Riemannian Spaces." Mathematics 7, no. 7 (July 15, 2019): 626. http://dx.doi.org/10.3390/math7070626.
Chen, Bang-Yen, and Lieven Vanhecke. "Reflections and symmetries in compact symmetric spaces." Bulletin of the Australian Mathematical Society 38, no. 3 (December 1988): 377–86. http://dx.doi.org/10.1017/s000497270002774x.
Chu, Cho-Ho. "JORDAN SYMMETRIC SPACES." Asian-European Journal of Mathematics 02, no. 03 (September 2009): 407–15. http://dx.doi.org/10.1142/s1793557109000339.
Kiosak, Volodymyr, Olexandr Lesechko, and Olexandr Latysh. "On geodesic mappings of symmetric pairs." Proceedings of the International Geometry Center 15, no. 3-4 (March 4, 2023): 230–38. http://dx.doi.org/10.15673/tmgc.v15i3-4.2430.
Mashimo, Katsuya, and Koji Tojo. "Circles in Riemannian symmetric spaces." Kodai Mathematical Journal 22, no. 1 (1999): 1–14. http://dx.doi.org/10.2996/kmj/1138043984.
Binh, T. Q. "On weakly symmetric Riemannian spaces." Publicationes Mathematicae Debrecen 42, no. 1-2 (January 1, 1993): 103–7. http://dx.doi.org/10.5486/pmd.1993.1281.
Dissertations / Theses on the topic "Riemannian symmetric spaces":
Osipova, Daria. "Symmetric submanifolds in symmetric spaces." Thesis, University of Hull, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.342976.
Yang, An. "Vector valued Poisson transforms on Riemannian symmetric spaces." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/33511.
Araujo, Fatima. "Einstein homogeneous Riemannian fibrations." Thesis, University of Edinburgh, 2008. http://hdl.handle.net/1842/4375.
Roby, Simon. "Résonances du Laplacien sur les fibrés vectoriels homogènes sur des espaces symétriques de rang réel un." Electronic Thesis or Diss., Université de Lorraine, 2021. http://www.theses.fr/2021LORR0129.
We study the resonances of the Laplacian acting on the compactly supported sections of a homogeneous vector bundle over a Riemannian symmetric space of the non- compact type. The symmetric space is assumed to have rank-one but the irreducible representation τ of the maximal compact K defining the vector bundle is arbitrary. We determine the resonances. Under the additional assumption that τ occurs in the spherical principal series, we determine the resonance representations. They are all irreducible. We find their Langlands parameters, their wave front sets and determine which of them are unitarizable
Vasconcelos, Rosa Tayane de. "O tensor de Ricci e campos de killing de espaços simétricos." reponame:Repositório Institucional da UFC, 2017. http://www.repositorio.ufc.br/handle/riufc/25968.
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Rejected by Rocilda Sales (rocilda@ufc.br), reason: Boa tarde, A Dissertação de ROSA TAYANE DE VASCONCELOS apresenta a alguns erros que devem corrigidos, os mesmos seguem listados abaixo: 1- EPÍGRAFE (coloque o nome do autor da epígrafe todo em letra maiúscula) 2- RESUMO/ ABSTRACT (retire o recuo dos parágrafos do resumo e do abstract) 3- PALAVRAS-CHAVE/ KEYWORDS (coloque a letra inicial do primeiro elemento das palavras- -chave e das Keywords em maiúscula) 4- CITAÇÕES (as citações a autores, que aparecem em todo o trabalho, não estão no padrão ABNT: se for apenas uma referência geral a uma obra, deve se colocar o último sobrenome do autor em letra maiúscula e o ano da publicação, ex.: EBERLEIN (2005). Caso seja a citação de um trecho particular da obra deve acrescentar o número da página, ex.: EBERLEIN (2005, p. 30). OBS.: as citações não devem estar entre colchetes. 5- TÍTULOS DOS CAPÍTULOS E SEÇÕES (coloque os títulos dos capítulos e seções em negrito) 6- REFERÊNCIAS (as referências bibliográficas não estão no padrão ABNT: apenas o último sobrenome do autor, que inicia a referência, deve estar em letra maiúscula, o restante do nome deve estar em letra minúscula. EX.: BROCKER, Theodor; TOM DIECK, Tammo. Representations of compact Lie groups, v. 98. Springer Science & Business Media, 2013. Atenciosamente, on 2017-09-18T15:04:06Z (GMT)
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This work brings a smooth and self-contained introduction to the study of the most basic aspects of symmetric spaces, having as its nal goal the characterization of the Killing vector fields and of the Ricci tensor of such riemannian manifolds. Several of the results presented in the initial chapter are not easily found, in the Diferential Geometry literature, in a way as accessible and self-contained as here. This being said, we believe that this work embodies some didactic relevance, for it others students interested in symmetric spaces a relatively smooth first contact. We shall generally look at symmetric spaces as homogeneous manifolds G=H, where G is a Lie group and H is a closed Lie subgroup of G, such that the natural mapping : G ! G=H is a riemannian submersion. Ultimately, this map allows us to describe the relationships between the curvature, the Ricci tensor and the geodesics of G and G=H. For our purposes, the crucial remark is that, under appropriate circumstances, one guarantees the existence, in G=H, of a metric for which left translations are isometries. Hence, a one-parameter family of such isometries gives rise to a Killing vector field, which turn into a Jacobi vector eld when restricted to a geodesic. We present explicit expressions for such Jacobi vector elds, showing that they only depend on the eigenvalues of the linear operator TX : g ! g given by TX = (adX)2, for certain vector elds X 2 g.
Este trabalho traz uma introdução suave e autocontida ao estudo dos aspectos mais básicos de espaços simétricos, tendo como objetivo final a caracterização dos campos de Killing e do tensor de Ricci de tais variedades riemannianas. Vários dos resultados obtidos nos capítulos iniciais não são encontrados, na literatura de Geometria Diferencial, de maneira tão acessível e autocontida como apresentados aqui. Com isso, acreditamos que o trabalho reveste-se de alguma relevância didática, por oferecer aos alunos interessados no estudo de espaços simétricos um primeiro contato relativamente suave. Em linhas gerais, veremos espaços simétricos como variedades homogêneas G=H, onde G e um grupo de Lie e H um subgrupo de Lie fechado de G, tais que a aplicação natural: G ! G=H seja uma submersão riemanniana. Através dela, descrevemos relações entre a curvatura, o tensor de Ricci e as geodésicas de G e G=H. Para nossos propósitos, a observação crucial e que, sob certas hipóteses, garantimos a existência, em G=H, de uma métrica cujas translações a esquerda são isometrias. Portanto, uma família a um parâmetro de tais isometrias d a origem a um campo de Killing que, por sua vez, restrito a geodésicas torna-se um campo de Jacobi. Apresentamos expressões para esses campos de Jacobi, mostrando que os mesmos só dependem dos autovalores do operador linear TX : g ! g dado por TX = (adX)2, para certos campos X 2 g.
Carvajales, Goyetche Leon Seibal. "Quantitative aspects of Anosov subgroups acting on symmetric spaces." Thesis, Sorbonne université, 2020. http://www.theses.fr/2020SORUS021.
This thesis addresses the study of the orbital counting problem for pseudo-Riemannian symmetric pairs under the action of Anosov subgroups of the underlying Lie group. In the first part we study this problem for the pair (PSO(p,q), PSO(p,q−1)) and a projective Anosov subgroup of PSO(p,q). We look at the orbit of a geodesic copy of the Riemannian symmetric space of PSO(p,q−1) inside the Riemannian symmetric space of PSO(p,q). We show a purely exponential asymptotic behavior, as t goes to infinity, for the number of elements in this orbit which are at distance at most t from the original geodesic copy. We then interpret this result as the asymptotic behavior of the amount of space-like geodesic segments (in the pseudo-Riemannian hyperbolic space) of maximum length t in the orbit of a basepoint. We prove analogue results for other related counting functions. In the second part we look at the pair (PSL(d,R), PSO(p,d−p)) and a Borel-Anosov subgroup of PSL(d,R), presenting contributions towards the understanding of the asymptotic behavior of the counting function associated to a geodesic copy of the Riemannian symmetric space of PSO(p,d-p) inside the Riemannian symmetric space of PSL(d,R)
Parthasarathy, Aprameyan [Verfasser], and Pablo [Akademischer Betreuer] Ramacher. "Analysis on the Oshima compactification of a Riemannian symmetric space of non-compact type / Aprameyan Parthasarathy. Betreuer: Pablo Ramacher." Marburg : Philipps-Universität Marburg, 2013. http://d-nb.info/1032314087/34.
Wang, Roy Chih Chung. "Adaptive Kernel Functions and Optimization Over a Space of Rank-One Decompositions." Thesis, Université d'Ottawa / University of Ottawa, 2017. http://hdl.handle.net/10393/36975.
Santos, Fábio Reis dos Santos. "Sobre a Geometria de Imersões Riemannianas." Universidade Federal da Paraíba, 2015. http://tede.biblioteca.ufpb.br:8080/handle/tede/8031.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
Our purpose is to study the geometry of Riemannian immersions in certain semi- Riemannian manifolds. Initially, considering linearWeingarten hypersurfaces immersed in locally symmetric manifolds and, imposing suitable constraints on the scalar curvature, we guarantee that such a hypersurface is either totally umbilical or isometric to a isoparametric hypersurface with two distinct principal curvatures, one of them being simple. In higher codimension, we use a Simons type formula to obtain new characterizations of hyperbolic cylinders through the study of submanifolds having parallel normalized mean curvature vector field in a semi-Riemannian space form. Finally, we investigate the rigidity of complete spacelike hypersurfaces immersed in the steady state space via applications of some maximum principles.
Nos propomos estudar a geometria de imersões Riemannianas em certas variedades semi-Riemannianas. Inicialmente, consideramos hipersuperfícies Weingarten lineares imersas em variedades localmente simétricas e, impondo restrições apropriadas à curvatura escalar, garantimos que uma tal hipersuperfície é totalmente umbílica ou isométrica a uma hipersuperfície isoparamétrica com duas curvaturas principais distintas, sendo uma destas simples. Em codimensão alta, usamos uma fórmula do tipo Simons para obter novas caracterizações de cilindros hiperbólicos a partir do estudo de subvariedades com vetor curvatura média normalizado paralelo em uma forma espacial semi-Riemanniana. Finalmente, investigamos a rigidez de hipersuperfícies tipo-espaço completas imersas no steady state space via aplicações de alguns princípios do máximo.
Vollmer, Andreas [Verfasser], Vladimir Jurʹevič [Gutachter] Matveev, Vsevolod V. [Gutachter] Shevchishin, and Boris I. [Gutachter] Kruglikov. "First integrals in stationary and axially symmetric space-times and sub-riemannian structures / Andreas Vollmer ; Gutachter: Vladimir Ju. Matveev, Vsevolod V. Shevchishin, Boris I. Kruglikov." Jena : Friedrich-Schiller-Universität Jena, 2016. http://d-nb.info/1177612852/34.
Books on the topic "Riemannian symmetric spaces":
Flensted-Jensen, Mogens. Analysis on non-Riemannian symmetric spaces. Providence, R.I: Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, 1986.
Burstall, Francis E., and John H. Rawnsley. Twistor Theory for Riemannian Symmetric Spaces. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/bfb0095561.
Borel, Armand. Semisimple Groups and Riemannian Symmetric Spaces. Gurgaon: Hindustan Book Agency, 1998. http://dx.doi.org/10.1007/978-93-80250-92-2.
Helgason, Sigurdur. Geometric analysis on symmetric spaces. 2nd ed. Providence, R.I: American Mathematical Society, 2008.
Helgason, Sigurdur. Geometric analysis on symmetric spaces. Providence, R.I: American Mathematical Society, 1994.
Kauffman, R. M. Eigenfunction expansions, operator algebras, and Riemannian symmetric spaces. Harlow, Essex, England: Addison Longman Ltd., 1996.
Burstall, Francis E. Twistor theory for Riemannian symmetric spaces: With applications to harmonic maps of Riemann surfaces. Berlin: Springer-Verlag, 1990.
Werner, Müller. L²-index of elliptic operators on manifolds with cusps of rank one. Berlin: Akademie der Wissenschaften der DDR, Karl-Weierstrass-Institut für Mathematik, 1985.
Krotz, Bernhard. The emage of the heat kernel transform fon Riemannian symmetric spaces of the noncompact type. Kyoto, Japan: Kyōto Daigaku Sūri Kaiseki Kenkyūjo, 2005.
Wolf, Joseph Albert. Spaces of constant curvature. 6th ed. Providence, R.I: AMS Chelsea Pub., 2011.
Book chapters on the topic "Riemannian symmetric spaces":
Borel, Armand. "Riemannian Symmetric Spaces." In Texts and Readings in Mathematics, 71–91. Gurgaon: Hindustan Book Agency, 1998. http://dx.doi.org/10.1007/978-93-80250-92-2_4.
Wolf, Joseph. "Riemannian symmetric spaces." In Harmonic Analysis on Commutative Spaces, 225–62. Providence, Rhode Island: American Mathematical Society, 2007. http://dx.doi.org/10.1090/surv/142/11.
Elworthy, K. David, Yves Le Jan, and Xue-Mei Li. "Example: Riemannian Submersions and Symmetric Spaces." In The Geometry of Filtering, 115–20. Basel: Springer Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0176-4_7.
Burstall, Francis E., and John H. Rawnsley. "Twistor lifts over Riemannian symmetric spaces." In Lecture Notes in Mathematics, 71–80. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/bfb0095568.
Verhóczki, László. "On Orbits of Symmetric Subgroups in Riemannian Symmetric Spaces." In New Developments in Differential Geometry, Budapest 1996, 485–501. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-5276-1_34.
Mashimo, Katsuya. "Totally Geodesic Surfaces of Riemannian Symmetric Spaces." In Springer Proceedings in Mathematics & Statistics, 301–8. Tokyo: Springer Japan, 2014. http://dx.doi.org/10.1007/978-4-431-55215-4_26.
Berndt, Jürgen. "Totally Geodesic Submanifolds of Riemannian Symmetric Spaces." In Springer Proceedings in Mathematics & Statistics, 33–42. Tokyo: Springer Japan, 2014. http://dx.doi.org/10.1007/978-4-431-55215-4_4.
Ban, E., M. Flensted-Jensen, and H. Schlichtkrull. "Basic Harmonic Analysis on Pseudo-Riemannian Symmetric Spaces." In Noncompact Lie Groups and Some of Their Applications, 69–101. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-1078-5_3.
Borel, Armand. "The L 2-Cohomology of Negatively Curved Riemannian Symmetric Spaces." In Springer Collected Works in Mathematics, 115–25. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-41240-0_7.
Falkowski, B. J. "Levy-Schoenberg kernels on riemannian symmetric spaces of noncompact type." In Lecture Notes in Mathematics, 58–67. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0077172.
Conference papers on the topic "Riemannian symmetric spaces":
Goze, Michel, and Elisabeth Remm. "RIEMANNIAN Γ-SYMMETRIC SPACES." In Proceedings of the VIII International Colloquium. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789814261173_0019.
Klein, Sebastian. "TOTALLY GEODESIC SUBMANIFOLDS IN RIEMANNIAN SYMMETRIC SPACES." In Proceedings of the VIII International Colloquium. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789814261173_0013.
OKUDA, Takayuki. "GEODESICS OF RIEMANNIAN SYMMETRIC SPACES INCLUDED IN REFLECTIVE SUBMANIFOLDS." In 5th International Colloquium on Differential Geometry and its Related Fields. WORLD SCIENTIFIC, 2017. http://dx.doi.org/10.1142/9789813220911_0002.
TASAKI, HIROYUKI. "CROFTON FORMULAE BY REFLECTIVE SUBMANIFOLDS IN RIEMANNIAN SYMMETRIC SPACES." In Proceedings of the 7th International Workshop on Complex Structures and Vector Fields. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701763_0025.
GILKEY, PETER B., and STANA NIKČEVIĆ. "COMPLETE K-CURVATURE HOMOGENEOUS PSEUDO-RIEMANNIAN MANIFOLDS 0-MODELED ON AN INDECOMPOSIBLE SYMMETRIC SPACE." In Proceedings in Honor of Professor K Sekigawa's 60th Birthday. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701701_0007.
Pokas, S., and I. Bilokobylskyi. "Lie group of the second degree infinitesimal conformal transformations in a symmetric Riemannian space of the first class." In APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 13th International Hybrid Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’21. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0100808.