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Опубліковано: 8 червня 2024

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Зміст

  1. Статті в журналах
  2. Дисертації
  3. Книги
  4. Частини книг
  5. Тези доповідей конференцій

Статті в журналах з теми "Riemannian symmetric spaces":

1

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.

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2

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.

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3

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.

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In this paper, we consider conformal mappings of Riemannian spaces onto Ricci-2-symmetric Riemannian spaces and geodesic mappings of spaces with affine connections onto Ricci-2-symmetric spaces. The main equations for the mappings are obtained as a closed system of Cauchy-type differential equations in covariant derivatives. We find the number of essential parameters which the solution of the system depends on. A similar approach was applied for the case of conformal mappings of Riemannian spaces onto Ricci-m-symmetric Riemannian spaces, as well as geodesic mappings of spaces with affine connections onto Ricci-m-symmetric spaces.
4

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.

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5

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.

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We consider conformal and concircular mappings of Eisenhart’s generalized Riemannian spaces. We prove conformal and concircular invariance of some tensors in Eisenhart’s generalized Riemannian spaces. We give new generalizations of symmetric spaces via Eisenhart’s generalized Riemannian spaces. Finally, we describe some properties of covariant derivatives of tensors analogous to Yano’s tensor of concircular curvature in Eisenhart symmetric spaces of various kinds.
6

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.

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Point symmetries and reflections are two important transformations on a Riemannian manifold. In this article we study the interactions between point symmetries and reflections in a compact symmetric space when the reflections are global isometries.
7

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.

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We introduce a class of Riemannian symmetric spaces, called Jordan symmetric spaces, which correspond to real Jordan triple systems and may be infinite dimensional. This class includes the symmetric R-spaces as well as the Hermitian symmetric spaces.
8

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.

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The paper treats properties of pseudo-Riemannian spaces admitting non-trivial geodesic mappings. A symmetric pair of pseudo-Riemannian spaces is a pair of spaces with coinciding values of covariant derivatives for their Riemann tensors. It is proved that the symmetric pair of pseudo-Riemannian spaces, which are not spaces of constant curvatures, are defined unequivocally by their geodesic lines. The research is carried out locally, using tensors, with no restrictions to the sign of the metric tensor and the signature of a space.
9

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.

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10

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.

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Дисертації з теми "Riemannian symmetric spaces":

1

Osipova, Daria. "Symmetric submanifolds in symmetric spaces." Thesis, University of Hull, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.342976.

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2

Yang, An. "Vector valued Poisson transforms on Riemannian symmetric spaces." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/33511.

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3

Araujo, Fatima. "Einstein homogeneous Riemannian fibrations." Thesis, University of Edinburgh, 2008. http://hdl.handle.net/1842/4375.

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This thesis is dedicated to the study of the existence of homogeneous Einstein metrics on the total space of homogeneous fibrations such that the fibers are totally geodesic manifolds. We obtain the Ricci curvature of an invariant metric with totally geodesic fibers and some necessary conditions for the existence of Einstein metrics with totally geodesic fibers in terms of Casimir operators. Some particular cases are studied, for instance, for normal base or fiber, symmetric fiber, Einstein base or fiber, for which the Einstein equations are manageable. We investigate the existence of such Einstein metrics for invariant bisymmetric fibrations of maximal rank, i.e., when both the base and the fiber are symmetric spaces and the base is an isotropy irreducible space of maximal rank. We find this way new Einstein metrics. For such spaces we describe explicitly the isotropy representation in terms subsets of roots and compute the eigenvalues of the Casimir operators of the fiber along the horizontal direction. Results for compact simply connected 4-symmetric spaces of maximal rank follow from this. Also, new invariant Einstein metrics are found on Kowalski n-symmetric spaces.
4

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.

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On étudie les résonances de l’opérateur de Laplace agissant sur les sections d’un fibré vectoriel homogène sur un espace symétrique Riemannien de type non-compact. On suppose que l’espace symétrique est de rang un, mais la représentation irréductible τ du compact maximal K, qui définit le fibré vectoriel, est quelconque. On détermine alors les résonances. Si on suppose de plus que τ apparaît dans les représentations de la série principale sphérique, on détermine les représentations issues des résonances. Elles sont toutes irréductibles. On trouve leurs paramètres de Langlands, leurs fronts d’onde et lesquelles sont unitarisables
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
5

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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VASCONCELOS, Rosa Tayane de. O tensor de Ricci e campos de killing de espaços simétricos. 2017. 81 f. Dissertação (Mestrado em Matemática)- Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2017.
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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.
6

Carvajales, Goyetche Leon Seibal. "Quantitative aspects of Anosov subgroups acting on symmetric spaces." Thesis, Sorbonne université, 2020. http://www.theses.fr/2020SORUS021.

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L’objet de cette thèse est l’étude du problème de comptage orbitale pour des couples symétriques pseudo-Riemanniens sous l’action des sous-groupes de type Anosov du groupe de Lie sous-jacent. Premièrement nous étudions ce problème pour le couple symétrique (PSO(p,q), PSO(p,q−1)) et un sous-groupe de PSO(p,q) de type projectivement Anosov . Nous regardons l’orbite d’une copie géodésique de l’espace symétrique Riemannien de PSO(p,q−1) dans l’espace symétrique Riemannien de PSO(p,q). Nous prouvons un comportement asymptotique purement exponentiel, lorsque t tend vers l’infini, pour le nombre d’éléments dans cette orbite qui sont à distance plus petit que t de la copie géodésique originale. Nous interprétons ce résultat comme le comportement asymptotique du nombre de segments géodésiques de type espace (dans l’espace hyperbolique pseudo-Riemannien) de longueur maximale t dans l’orbite d’un point base. Nous prouvons des résultats analogues pour d’autres fonctions de comptage. Ensuite nous regardons le couple symétrique (PSL(d,R), PSO(p,d−p)) et un sous-groupe Borel-Anosov de PSL(d,R). Nous présentons des contributions vers la compréhension du comportement asymptotique de la fonction de comptage associée à une copie géodésique de l’espace symétrique Riemannien de PSO(p,d-p) dans l’espace symétrique Riemannien de PSL(d,R)
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)
7

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.

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8

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.

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The representer theorem from the reproducing kernel Hilbert space theory is the origin of many kernel-based machine learning and signal modelling techniques that are popular today. Most kernel functions used in practical applications behave in a homogeneous manner across the domain of the signal of interest, and they are called stationary kernels. One open problem in the literature is the specification of a non-stationary kernel that is computationally tractable. Some recent works solve large-scale optimization problems to obtain such kernels, and they often suffer from non-identifiability issues in their optimization problem formulation. Many practical problems can benefit from using application-specific prior knowledge on the signal of interest. For example, if one can adequately encode the prior assumption that edge contours are smooth, one does not need to learn a finite-dimensional dictionary from a database of sampled image patches that each contains a circular object in order to up-convert images that contain circular edges. In the first portion of this thesis, we present a novel method for constructing non-stationary kernels that incorporates prior knowledge. A theorem is presented that ensures the result of this construction yields a symmetric and positive-definite kernel function. This construction does not require one to solve any non-identifiable optimization problems. It does require one to manually design some portions of the kernel while deferring the specification of the remaining portions to when an observation of the signal is available. In this sense, the resultant kernel is adaptive to the data observed. We give two examples of this construction technique via the grayscale image up-conversion task where we chose to incorporate the prior assumption that edge contours are smooth. Both examples use a novel local analysis algorithm that summarizes the p-most dominant directions for a given grayscale image patch. The non-stationary properties of these two types of kernels are empirically demonstrated on the Kodak image database that is popular within the image processing research community. Tensors and tensor decomposition methods are gaining popularity in the signal processing and machine learning literature, and most of the recently proposed tensor decomposition methods are based on the tensor power and alternating least-squares algorithms, which were both originally devised over a decade ago. The algebraic approach for the canonical polyadic (CP) symmetric tensor decomposition problem is an exception. This approach exploits the bijective relationship between symmetric tensors and homogeneous polynomials. The solution of a CP symmetric tensor decomposition problem is a set of p rank-one tensors, where p is fixed. In this thesis, we refer to such a set of tensors as a rank-one decomposition with cardinality p. Existing works show that the CP symmetric tensor decomposition problem is non-unique in the general case, so there is no bijective mapping between a rank-one decomposition and a symmetric tensor. However, a proposition in this thesis shows that a particular space of rank-one decompositions, SE, is isomorphic to a space of moment matrices that are called quasi-Hankel matrices in the literature. Optimization over Riemannian manifolds is an area of optimization literature that is also gaining popularity within the signal processing and machine learning community. Under some settings, one can formulate optimization problems over differentiable manifolds where each point is an equivalence class. Such manifolds are called quotient manifolds. This type of formulation can reduce or eliminate some of the sources of non-identifiability issues for certain optimization problems. An example is the learning of a basis for a subspace by formulating the solution space as a type of quotient manifold called the Grassmann manifold, while the conventional formulation is to optimize over a space of full column rank matrices. The second portion of this thesis is about the development of a general-purpose numerical optimization framework over SE. A general-purpose numerical optimizer can solve different approximations or regularized versions of the CP decomposition problem, and they can be applied to tensor-related applications that do not use a tensor decomposition formulation. The proposed optimizer uses many concepts from the Riemannian optimization literature. We present a novel formulation of SE as an embedded differentiable submanifold of the space of real-valued matrices with full column rank, and as a quotient manifold. Riemannian manifold structures and tangent space projectors are derived as well. The CP symmetric tensor decomposition problem is used to empirically demonstrate that the proposed scheme is indeed a numerical optimization framework over SE. Future investigations will concentrate on extending the proposed optimization framework to handle decompositions that correspond to non-symmetric tensors.
9

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.
10

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.

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Книги з теми "Riemannian symmetric spaces":

1

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.

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2

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.

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3

Borel, Armand. Semisimple Groups and Riemannian Symmetric Spaces. Gurgaon: Hindustan Book Agency, 1998. http://dx.doi.org/10.1007/978-93-80250-92-2.

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4

Helgason, Sigurdur. Geometric analysis on symmetric spaces. 2nd ed. Providence, R.I: American Mathematical Society, 2008.

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5

Helgason, Sigurdur. Geometric analysis on symmetric spaces. Providence, R.I: American Mathematical Society, 1994.

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6

Kauffman, R. M. Eigenfunction expansions, operator algebras, and Riemannian symmetric spaces. Harlow, Essex, England: Addison Longman Ltd., 1996.

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7

Burstall, Francis E. Twistor theory for Riemannian symmetric spaces: With applications to harmonic maps of Riemann surfaces. Berlin: Springer-Verlag, 1990.

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8

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.

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9

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.

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10

Wolf, Joseph Albert. Spaces of constant curvature. 6th ed. Providence, R.I: AMS Chelsea Pub., 2011.

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Частини книг з теми "Riemannian symmetric spaces":

1

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.

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2

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.

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3

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.

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4

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.

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5

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.

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6

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.

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7

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.

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8

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.

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9

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.

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10

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.

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Тези доповідей конференцій з теми "Riemannian symmetric spaces":

1

Goze, Michel, та Elisabeth Remm. "RIEMANNIAN Γ-SYMMETRIC SPACES". У Proceedings of the VIII International Colloquium. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789814261173_0019.

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2

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.

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3

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.

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4

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.

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5

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.

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6

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.

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