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Статті в журналах з теми "Locally homogenous spaces"

Автор: Grafiati

Опубліковано: 10 березня 2023

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1

Rejali, Ali, and Navid Sabzali. "On the homological and algebraical properties of some Feichtinger algebras." Mathematica Slovaca 71, no. 5 (October 1, 2021): 1211–28. http://dx.doi.org/10.1515/ms-2021-0049.

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Анотація:

Abstract Let G be a locally compact group (not necessarily abelian) and B be a homogeneous Banach space on G, which is in a good situation with respect to a homogeneous function algebra on G. Feichtinger showed that there exists a minimal Banach space B min in the family of all homogenous Banach spaces C on G, containing all elements of B with compact support. In this paper, the amenability and super amenability of B min with respect to the convolution product or with respect to the pointwise product are showed to correspond to amenability, discreteness or finiteness of the group G and conversely. We also prove among other things that B min is a symmetric Segal subalgebra of L 1(G) on an IN-group G, under certain conditions, and we apply our results to study pseudo-amenability and some other homological properties of B min on IN-groups. Furthermore, we determine necessary and sufficient conditions on A under which A min $\mathcal{A}_{\min}$ with the pointwise product is an abstract Segal algebra or Segal algebra in A, whenever A is a homogeneous function algebra with an approximate identity. We apply these results to study amenability of some Feichtinger algebras with respect to the pointwise product.

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2

Rejali, Ali, and Navid Sabzali. "On the homological and algebraical properties of some Feichtinger algebras." Mathematica Slovaca 71, no. 5 (October 1, 2021): 1211–28. http://dx.doi.org/10.1515/ms-2021-0049.

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Анотація:

Abstract Let G be a locally compact group (not necessarily abelian) and B be a homogeneous Banach space on G, which is in a good situation with respect to a homogeneous function algebra on G. Feichtinger showed that there exists a minimal Banach space B min in the family of all homogenous Banach spaces C on G, containing all elements of B with compact support. In this paper, the amenability and super amenability of B min with respect to the convolution product or with respect to the pointwise product are showed to correspond to amenability, discreteness or finiteness of the group G and conversely. We also prove among other things that B min is a symmetric Segal subalgebra of L 1(G) on an IN-group G, under certain conditions, and we apply our results to study pseudo-amenability and some other homological properties of B min on IN-groups. Furthermore, we determine necessary and sufficient conditions on A under which A min $\mathcal{A}_{\min}$ with the pointwise product is an abstract Segal algebra or Segal algebra in A, whenever A is a homogeneous function algebra with an approximate identity. We apply these results to study amenability of some Feichtinger algebras with respect to the pointwise product.

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3

Seidel, Hans Peter. "Locally homogeneous ANR-spaces." Archiv der Mathematik 44, no. 1 (January 1985): 79–81. http://dx.doi.org/10.1007/bf01193784.

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4

Ancel, Fredric D., and David P. Bellamy. "On homogeneous locally conical spaces." Fundamenta Mathematicae 241, no. 1 (2018): 1–15. http://dx.doi.org/10.4064/fm282-4-2017.

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5

Deng, Shaoqiang, and Joseph A. Wolf. "Locally Symmetric Homogeneous Finsler Spaces." International Mathematics Research Notices 2013, no. 18 (July 24, 2012): 4223–42. http://dx.doi.org/10.1093/imrn/rns179.

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6

Rodionov, E. D., V. V. Slavskiĭ, and L. N. Chibrikova. "Locally conformally homogeneous pseudo-Riemannian spaces." Siberian Advances in Mathematics 17, no. 3 (September 2007): 186–212. http://dx.doi.org/10.3103/s1055134407030030.

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7

Nedela, Roman. "Covering spaces of locally homogeneous graphs." Discrete Mathematics 121, no. 1-3 (October 1993): 177–88. http://dx.doi.org/10.1016/0012-365x(93)90550-d.

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8

Fox, Jeffrey, and Peter Haskell. "Index theory on locally homogeneous spaces." K-Theory 4, no. 6 (November 1990): 547–68. http://dx.doi.org/10.1007/bf00538884.

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9

Berestovskiǐ, V. N., Denise M. Halverson, and Dušan Repovš. "Locally G-homogeneous Busemann G-spaces." Differential Geometry and its Applications 29, no. 3 (June 2011): 299–318. http://dx.doi.org/10.1016/j.difgeo.2011.03.001.

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10

Andruchow, Esteban, and Lázaro Recht. "Larotonda spaces: Homogeneous spaces and conditional expectations." International Journal of Mathematics 27, no. 02 (February 2016): 1650002. http://dx.doi.org/10.1142/s0129167x16500026.

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Анотація:

We define a Larotonda space as a quotient space [Formula: see text] of the unitary groups of [Formula: see text]-algebras [Formula: see text] with a faithful unital conditional expectation [Formula: see text] In particular, [Formula: see text] is complemented in [Formula: see text], a fact which implies that [Formula: see text] has [Formula: see text] differentiable structure, with the topology induced by the norm of [Formula: see text]. The conditional expectation also allows one to define a reductive structure (in particular, a linear connection) and a [Formula: see text]-invariant Finsler metric in [Formula: see text]. Given a point [Formula: see text] and a tangent vector [Formula: see text], we consider the problem of whether the geodesic [Formula: see text] of the linear connection satisfying these initial data is (locally) minimal for the metric. We find a sufficient condition. Several examples are given, of locally minimal geodesics.

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11

Fels, G. "A note on homogeneous locally symmetric spaces." Transformation Groups 2, no. 3 (September 1997): 269–77. http://dx.doi.org/10.1007/bf01234660.

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12

Spiro, Andrea. "A remark on locally homogeneous Riemannian spaces." Results in Mathematics 24, no. 3-4 (November 1993): 318–25. http://dx.doi.org/10.1007/bf03322340.

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13

KATSUDA, Atsushi. "A pinching problem for locally homogeneous spaces." Journal of the Mathematical Society of Japan 41, no. 1 (January 1989): 57–74. http://dx.doi.org/10.2969/jmsj/04110057.

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14

Bramanti, Marco, and Maochun Zhu. "Local real analysis in locally homogeneous spaces." Manuscripta Mathematica 138, no. 3-4 (November 9, 2011): 477–528. http://dx.doi.org/10.1007/s00229-011-0501-6.

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15

Mirotin, Adolf R. "Hausdorff operators on homogeneous spaces of locally compact groups." Journal of the Belarusian State University. Mathematics and Informatics, no. 2 (July 30, 2020): 28–35. http://dx.doi.org/10.33581/2520-6508-2020-2-28-35.

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Анотація:

Hausdorff operators on the real line and multidimensional Euclidean spaces originated from some classical summation methods. Now it is an active research area. Hausdorff operators on general groups were defined and studied by the author since 2019. The purpose of this paper is to define and study Hausdorff operators on Lebesgue and real Hardy spaces over homogeneous spaces of locally compact groups. We introduce in particular an atomic Hardy space over homogeneous spaces of locally compact groups and obtain conditions for boundedness of Hausdorff operators on such spaces. Several corollaries are considered and unsolved problems are formulated.

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16

Carroy, Raphaël, Andrea Medini, and Sandra Müller. "Every zero-dimensional homogeneous space is strongly homogeneous under determinacy." Journal of Mathematical Logic 20, no. 03 (March 4, 2020): 2050015. http://dx.doi.org/10.1142/s0219061320500154.

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Анотація:

All spaces are assumed to be separable and metrizable. We show that, assuming the Axiom of Determinacy, every zero-dimensional homogeneous space is strongly homogeneous (i.e. all its non-empty clopen subspaces are homeomorphic), with the trivial exception of locally compact spaces. In fact, we obtain a more general result on the uniqueness of zero-dimensional homogeneous spaces which generate a given Wadge class. This extends work of van Engelen (who obtained the corresponding results for Borel spaces), complements a result of van Douwen, and gives partial answers to questions of Terada and Medvedev.

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17

Boyd, Christopher. "Nuclear and integral polynomials on testing $\mathsf C^{(I)}, \;\; I$ uncountable." MATHEMATICA SCANDINAVICA 93, no. 2 (December 1, 2003): 313. http://dx.doi.org/10.7146/math.scand.a-14426.

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Анотація:

We show that for $I$ an uncountable index set and $n\ge 3$ the spaces of all $n$-homogeneous polynomials, all $n$-homogeneous integral polynomials and all $n$-homogeneous nuclear polynomials are all different. Using this result we then show that the class of locally Asplund spaces is not preserved under uncountable locally convex direct sums nor is separably determined.

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18

Al-Homoud, Majd, and Hala Ghanem. "Regeneration of Amman Center - Social Acceptance of Syrian Migrants in Downtown Amman." Resourceedings 2, no. 1 (February 25, 2019): 27. http://dx.doi.org/10.21625/resourceedings.v2i1.450.

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Анотація:

Several studies discussed attitudes towards migrants; some of the issues pointed out are integration that requires interaction between migrants and the host society. Homogenous social groupings produce stronger communities. As the conflict in Syria entered its fifth year, Jordan hosted about 1.4 million registered Syrians, of whom 646,700 are informal refugees. Eighty-five percent of the refugees live outside camps in some of the poorest areas of Jordan. Consequently, new household’s typologies pressured the supply side. Such non-camp refugees’ migration patterns and housing market conditions formed ethnic homogeneous enclaves in different locations in Amman. Accordingly, non-camp refugees occupied and rented the upper floors of mixed used commercial buildings in downtown Amman.The present study investigated social acceptance of Syrian migrants residing in upper floors of commercial mixed used buildings located in the city center of Amman. The primary purpose of this research is to study how social acceptance of Syrian migrants is influenced by social gating. The hypothesis of the present study states that social acceptance of Syrian migrants in downtown Amman is influenced by sense of merchants’ sense of social gating. The significance of the study stems from that the development of downtown Amman with such rich social context can be informative and useful for strategic planners, local governments, NGO’s, social workers, and psychologists. This paper offers such an opportunity to reflect on an unfolding crisis that is of major social concern with changing urban demographics.The study was conducted using a quantitative and qualitative research strategy; an embedded research design was used. The quantitative method was conducted using a survey with downtown merchants, in addition to supportive qualitative methods of face-to-face interviews. The study was conducted in the central part of Amman, known locally as Wast Al-balad, which is considered the old commercial area that dates back to the second quarter of the twentieth century. Some of these secondary residential units became spaces (enclaves) for migrants that formed ethnic low-income enclaves. In the last five years, low-income Syrian migrants started to rent these units in Amman’s urban center. Outcomes indicated that social cohesion is the strongest motivator for acceptance of outsiders by the local merchants to reside in the upper floors of the commercial buildings of Downtown Amman area.

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19

Milla, van. "Countable dense homogeneous rimcompact spaces and local connectivity." Filomat 29, no. 1 (2015): 179–82. http://dx.doi.org/10.2298/fil1501179m.

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Анотація:

We prove that every nonmeager connected Countable Dense Homogeneous space is locally connected under some additional mild connectivity assumption. As a corollary we obtain that every Countable Dense Homogeneous connected rimcompact space is locally connected.

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20

Parthasarathy, K., and N. Shravan Kumar. "Feichtinger's Segal algebra on homogeneous spaces." International Journal of Mathematics 26, no. 08 (July 2015): 1550054. http://dx.doi.org/10.1142/s0129167x15500548.

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Анотація:

Let K be a compact subgroup of a locally compact group G. We extend to the context of homogeneous spaces, G/K, the definition of Feichtinger's Segal algebra. The functorial properties of the Segal algebra are proved.

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21

Mishin, S. N. "Homogeneous differential-operator equations in locally convex spaces." Russian Mathematics 61, no. 1 (January 2017): 22–38. http://dx.doi.org/10.3103/s1066369x17010042.

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22

Onneweer, C., and Su Weiyi. "Homogeneous Besov spaces on locally compact Vilenkin groups." Studia Mathematica 93, no. 1 (1989): 17–39. http://dx.doi.org/10.4064/sm-93-1-17-39.

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23

Hrušák, Michael, and Jan van Mill. "Nearly Countable Dense Homogeneous Spaces." Canadian Journal of Mathematics 66, no. 4 (August 1, 2014): 743–58. http://dx.doi.org/10.4153/cjm-2013-006-8.

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AbstractWe study separable metric spaces with few types of countable dense sets. We present a structure theorem for locally compact spaces having precisely n types of countable dense sets: such a space contains a subset S of size at most n−1 such that S is invariant under all homeomorphisms of X and X ∖ S is countable dense homogeneous. We prove that every Borel space having fewer than c types of countable dense sets is Polish. The natural question of whether every Polish space has either countably many or c many types of countable dense sets is shown to be closely related to Topological Vaught's Conjecture.

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24

Calvaruso, G., and L. Vanhecke. "Semi-symmetric ball-homogeneous spaces and a volume conjecture." Bulletin of the Australian Mathematical Society 57, no. 1 (February 1998): 109–15. http://dx.doi.org/10.1017/s0004972700031452.

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We prove that semi-symmetric ball-homogeneous spaces are locally symmetric and we use this result to prove that a semi-symmetric Riemannian manifold such that the volume of each sufficiently small geodesic ball is the same as in a Euclidean space, is locally flat.

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25

Gundyrev, I. A. "On similarity homogeneous locally compact spaces with intrinsic metric." Russian Mathematics 52, no. 4 (April 2008): 24–37. http://dx.doi.org/10.3103/s1066369x0804004x.

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26

Bandt, Christoph, and Gebreselassie Baraki. "Metrically invariant measures on locally homogeneous spaces and hyperspaces." Pacific Journal of Mathematics 121, no. 1 (January 1, 1986): 13–28. http://dx.doi.org/10.2140/pjm.1986.121.13.

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27

Labourie, F., S. Mozes, and R. J. Zimmer. "On manifolds locally modelled on non-riemannian homogeneous spaces." Geometric and Functional Analysis 5, no. 6 (November 1995): 955–65. http://dx.doi.org/10.1007/bf01902217.

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28

Pavlović, Miroslav, and Juhani Riihentaus. "Quasi-nearly subharmonic functions in locally uniformly homogeneous spaces." Positivity 15, no. 1 (November 25, 2009): 1–10. http://dx.doi.org/10.1007/s11117-009-0037-0.

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29

Berestovskii, V. N. "Structure of homogeneous locally compact spaces with intrinsic metric." Siberian Mathematical Journal 30, no. 1 (January 1989): 16–25. http://dx.doi.org/10.1007/bf01054211.

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30

Lauret, Jorge, and Cynthia E. Will. "Prescribing Ricci curvature on homogeneous spaces." Journal für die reine und angewandte Mathematik (Crelles Journal) 2022, no. 783 (January 6, 2022): 95–133. http://dx.doi.org/10.1515/crelle-2021-0069.

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Анотація:

Abstract The prescribed Ricci curvature problem in the context of G-invariant metrics on a homogeneous space M = G / K {M=G/K} is studied. We focus on the metrics at which the map g ↦ Rc ⁡ ( g ) {g\mapsto\operatorname{Rc}(g)} is, locally, as injective and surjective as it can be. Our main result is that such property is generic in the compact case. Our main tool is a formula for the Lichnerowicz Laplacian we prove in terms of the moment map for the variety of algebras.

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31

Kowalski, Oldřich. "A classification of Riemannian 3-manifolds with constant principal ricci curvaturesρ1= ρ2≠ ρ3". Nagoya Mathematical Journal 132 (грудень 1993): 1–36. http://dx.doi.org/10.1017/s002776300000461x.

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Анотація:

This paper has been motivated by various problems and results in differential geometry. The main motivation is the study of curvature homogeneous Riemannian spaces initiated in 1960 by I.M. Singer (see Section 9—Appendix for the precise definitions and references). Up to recently, only sporadic classes of examples have been known of curvature homogeneous spaces which are not locally homogeneous. For instance, isoparametric hypersurfaces in space forms give nice examples of nontrivial curvature homogeneous spaces (see [FKM]). To study the topography of curvature homogeneous spaces more systematically, it is natural to start with the dimension n = 3. The following results and problems have been particularly inspiring.

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32

Nishihara, Masaru, and Kwang Ho Shon. "The Tensor Product Representation of Polynomials of Weak Type in a DF-Space." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/795016.

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LetEandFbe locally convex spaces overCand letP(nE;F)be the space of all continuousn-homogeneous polynomials fromEtoF. We denote by⨂n,s,πEthen-fold symmetric tensor product space ofEendowed with the projective topology. Then, it is well known that each polynomialp∈P(nE;F)is represented as an element in the spaceL(⨂n,s,πE;F)of all continuous linear mappings from⨂n,s,πEtoF. A polynomialp∈P(nE;F)is said to beof weak typeif, for every bounded setBofE,p|Bis weakly continuous onB. We denote byPw(nE;F)the space of alln-homogeneous polynomials of weak type fromEtoF. In this paper, in case thatEis a DF space, we will give the tensor product representation of the spacePw(nE;F).

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33

Lu, Shanzhen, and Dachun Yang. "Some non-homogeneous Hardy spaces on locally compact Vilenkin groups." Colloquium Mathematicum 69, no. 1 (1996): 1–17. http://dx.doi.org/10.4064/cm-69-1-1-17.

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34

Das, Sanjit, Kartik Prabhu, and Sayan Kar. "Higher order geometric flows on three-dimensional locally homogeneous spaces." Journal of Mathematical Physics 54, no. 1 (January 2013): 013509. http://dx.doi.org/10.1063/1.4773577.

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35

Einsiedler, Manfred, and Elon Lindenstrauss. "Joinings of higher-rank diagonalizable actions on locally homogeneous spaces." Duke Mathematical Journal 138, no. 2 (June 2007): 203–32. http://dx.doi.org/10.1215/s0012-7094-07-13822-5.

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36

Niemiec, Piotr, and Piotr Pikul. "Hyperbolic Geometry For Non-Differential Topologists." Mathematica Slovaca 72, no. 1 (February 1, 2022): 165–84. http://dx.doi.org/10.1515/ms-2022-0012.

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Анотація:

Abstract A soft presentation of hyperbolic spaces (as metric spaces), free of differential apparatus, is offered. Fifth Euclid’s postulate in such spaces is overthrown and, among other things, it is proved that spheres (equipped with great-circle distances) and hyperbolic and Euclidean spaces are the only locally compact geodesic (i.e., convex) metric spaces that are three-point homogeneous.

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37

Al Ghour, Samer, and Nahed Al Khatib. "On some types of slight homogeneity." International Journal of Electrical and Computer Engineering (IJECE) 10, no. 4 (August 1, 2020): 4305. http://dx.doi.org/10.11591/ijece.v10i4.pp4305-4312.

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Анотація:

As a generalization of the concept SLH space, we introduce the concept of slightly strongly locally homogeneous (SSLH) spaces. Also, we introduce the concepts of slightly dense set as well as slightly separable space, and use them to introduce two new types of slightly countable dense homogeneous spaces. Several results, relationships, examples and counter-examples concerning these concepts are obtained.

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38

ESMAEELZADEH, F., R. A. KAMYABI GOL, and R. RAISI TOUSI. "ON THE CONTINUOUS WAVELET TRANSFORM ON HOMOGENEOUS SPACES." International Journal of Wavelets, Multiresolution and Information Processing 10, no. 04 (July 2012): 1250038. http://dx.doi.org/10.1142/s0219691312500385.

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Анотація:

Let G be a locally compact group with a compact subgroup H. We define a square integrable representation of a homogeneous space G/H on a Hilbert space [Formula: see text]. The reconstruction formula for G/H is established and as a result it is concluded that the set of admissible vectors is path connected. The continuous wavelet transform on G/H is defined and it is shown that the range of the continuous wavelet transform is a reproducing kernel Hilbert space. Moreover, we obtain a necessary and sufficient condition for the continuous wavelet transform to be onto.

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39

Bramanti, Marco, and Maria Stella Fanciullo. "The local sharp maximal function and BMO on locally homogeneous spaces." Annales Academiae Scientiarum Fennicae Mathematica 42 (February 2017): 453–72. http://dx.doi.org/10.5186/aasfm.2017.4229.

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40

Pianzola, A. "Locally trivial principal homogeneous spaces and conjugacy theorems for Lie algebras." Journal of Algebra 275, no. 2 (May 2004): 600–614. http://dx.doi.org/10.1016/s0021-8693(03)00399-5.

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41

Lauret, Emilio A., and Roberto J. Miatello. "Strong multiplicity one theorems for locally homogeneous spaces of compact-type." Proceedings of the American Mathematical Society 148, no. 7 (March 2, 2020): 3163–73. http://dx.doi.org/10.1090/proc/14980.

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42

Masuda, Kayo. "Homogeneous locally nilpotent derivations having slices and embeddings of affine spaces." Journal of Algebra 321, no. 6 (March 2009): 1719–33. http://dx.doi.org/10.1016/j.jalgebra.2008.12.012.

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43

Giudici, Michael, Cai Heng Li, and Cheryl E. Praeger. "Locally 2-arc transitive graphs, homogeneous factorizations, and partial linear spaces." Journal of Combinatorial Designs 14, no. 2 (March 2006): 139–48. http://dx.doi.org/10.1002/jcd.20072.

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44

Yamato, Kazuo. "A characterization of locally homogeneous Riemann manifolds of dimension 3." Nagoya Mathematical Journal 123 (September 1991): 77–90. http://dx.doi.org/10.1017/s0027763000003652.

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Анотація:

It is classical to characterize locally homogeneous Riemann manifolds by infinitesimal conditions. For example, [Si] asserts that the local-homogeneity is equivalent to the existence of linear isometries between tangent spaces which preserve the curvatures and their covariant derivatives up to certain orders. It is also known that the local homogeneity is equivalent to the existence of a certain tensor field of type (1, 2) (for this and a further study, see [TV]).

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45

Andreeva, Tatiana A., Dmitry N. Oskorbin, and Evgeny D. Rodionov. "Investigation of conformally killing vector fields on 5-dimensional 2-symmetric lorentzian manifolds." Yugra State University Bulletin 60, no. 1 (December 23, 2021): 17–22. http://dx.doi.org/10.17816/byusu20210117-22.

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Анотація:

Conformally Killing fields play an important role in the theory of Ricci solitons and also generate an important class of locally conformally homogeneous (pseudo) Riemannian manifolds. In the Riemannian case, V. V. Slavsky and E.D. Rodionov proved that such spaces are either conformally flat or conformally equivalent to locally homogeneous Riemannian manifolds. In the pseudo-Riemannian case, the question of their structure remains open. Pseudo-Riemannian symmetric spaces of order k, where k 2, play an important role in research in pseudo-Riemannian geometry. Currently, they have been investigated in cases k=2,3 by D.V. Alekseevsky, A.S. Galaev and others. For arbitrary k, non-trivial examples of such spaces are known: generalized Kachen - Wallach manifolds. In the case of small dimensions, these spaces and Killing vector fields on them were studied by D.N. Oskorbin, E.D. Rodionov, and I.V. Ernst with the helpof systems of computer mathematics. In this paper, using the Sagemath SCM, we investigate conformally Killing vector fields on five-dimensional indecomposable 2- symmetric Lorentzian manifolds, and construct an algorithm for their computation.

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46

Haji-Badali, Ali, and Amirhesam Zaeim. "Commutative curvature operators over four-dimensional homogeneous manifolds." International Journal of Geometric Methods in Modern Physics 12, no. 10 (October 25, 2015): 1550123. http://dx.doi.org/10.1142/s0219887815501236.

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Four-dimensional pseudo-Riemannian homogeneous spaces whose isotropy is non-trivial with commuting curvature operators have been studied. The only example of homogeneous Einstein four-manifold which is curvature-Ricci commuting but not semi-symmetric has been presented. Non-trivial examples of semi-symmetric homogeneous four-manifolds which are not locally symmetric, also Jacobi–Jacobi commuting manifolds which are not flat have been presented.

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47

YOSHINO, TARO. "CRITERION OF PROPER ACTIONS ON HOMOGENEOUS SPACES OF CARTAN MOTION GROUPS." International Journal of Mathematics 18, no. 03 (March 2007): 245–54. http://dx.doi.org/10.1142/s0129167x07004035.

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The Cartan motion group associated to a Riemannian symmetric space X is a semidirect product group acting isometrically on its tangent space. For two subsets in a locally compact group G, Kobayashi introduced the concept of "properness" as a generalization of properly discontinuous actions of discrete subgroups on homogeneous spaces of G. In this paper, we give a criterion of properness for homogeneous spaces of Cartan motion groups. Our criterion has a similar feature to the case where G is a reductive Lie group.

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48

Agricola, Ilka, Giulia Dileo та Leander Stecker. "Homogeneous non-degenerate 3-(α,δ)-Sasaki manifolds and submersions over quaternionic Kähler spaces". Annals of Global Analysis and Geometry 60, № 1 (26 квітня 2021): 111–41. http://dx.doi.org/10.1007/s10455-021-09762-9.

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AbstractWe show that every 3-$$(\alpha ,\delta )$$ ( α , δ ) -Sasaki manifold of dimension $$4n + 3$$ 4 n + 3 admits a locally defined Riemannian submersion over a quaternionic Kähler manifold of scalar curvature $$16n(n+2)\alpha \delta$$ 16 n ( n + 2 ) α δ . In the non-degenerate case we describe all homogeneous 3-$$(\alpha ,\delta )$$ ( α , δ ) -Sasaki manifolds fibering over symmetric Wolf spaces and over their non-compact dual symmetric spaces. If $$\alpha \delta > 0$$ α δ > 0 , this yields a complete classification of homogeneous 3-$$(\alpha ,\delta )$$ ( α , δ ) -Sasaki manifolds. For $$\alpha \delta < 0$$ α δ < 0 , we provide a general construction of homogeneous 3-$$(\alpha , \delta )$$ ( α , δ ) -Sasaki manifolds fibering over non-symmetric Alekseevsky spaces, the lowest possible dimension of such a manifold being 19.

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49

Gundyrev, I. A. "The structure of similarity homogeneous locally compact spaces with an intrinsic metric." Siberian Advances in Mathematics 25, no. 1 (January 2015): 33–38. http://dx.doi.org/10.3103/s1055134415010046.

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50

Papadopoulos, G. O., and Th Grammenos. "Locally homogeneous spaces, induced Killing vector fields and applications to Bianchi prototypes." Journal of Mathematical Physics 53, no. 7 (July 2012): 072502. http://dx.doi.org/10.1063/1.4732119.

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