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Journal articles on the topic 'Cohomogeneity'

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Author: Grafiati

Published: 10 March 2023

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Fujioka, Atsushi, and Hitoshi Furuhata. "Centroaffine Surfaces of Cohomogeneity One." Bulletin of the Brazilian Mathematical Society, New Series 50, no. 1 (September 28, 2018): 291–313. http://dx.doi.org/10.1007/s00574-018-0120-x.

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12

Dammerman, Brandon. "Diagonalizing cohomogeneity-one Einstein metrics." Journal of Geometry and Physics 59, no. 9 (September 2009): 1271–84. http://dx.doi.org/10.1016/j.geomphys.2009.06.010.

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13

Buttsworth, Timothy. "Cohomogeneity-one quasi-Einstein metrics." Journal of Mathematical Analysis and Applications 470, no. 1 (February 2019): 201–17. http://dx.doi.org/10.1016/j.jmaa.2018.09.064.

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14

Galaz-García, Fernando, and Masoumeh Zarei. "Cohomogeneity one topological manifolds revisited." Mathematische Zeitschrift 288, no. 3-4 (August 20, 2017): 829–53. http://dx.doi.org/10.1007/s00209-017-1915-y.

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15

Ahmadi, P. "Cohomogeneity One Dynamics on Three Dimensional Minkowski Space." Zurnal matematiceskoj fiziki, analiza, geometrii 15, no. 2 (September 25, 2016): 155–69. http://dx.doi.org/10.15407/mag15.02.155.

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16

Böhm, Christoph. "Non-compact cohomogeneity one Einstein manifolds." Bulletin de la Société mathématique de France 127, no. 1 (1999): 135–77. http://dx.doi.org/10.24033/bsmf.2345.

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17

Morisawa, Yoshiyuki, Soichi Hasegawa, Tatsuhiko Koike, and Hideki Ishihara. "Cohomogeneity-one-string integrability of spacetimes." Classical and Quantum Gravity 36, no. 15 (July 17, 2019): 155009. http://dx.doi.org/10.1088/1361-6382/ab2e28.

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18

Berndt, Jürgen, and Martina Brück. "Cohomogeneity one actions on hyperbolic spaces." Journal für die reine und angewandte Mathematik (Crelles Journal) 2001, no. 541 (January 23, 2001): 209–35. http://dx.doi.org/10.1515/crll.2001.093.

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19

Goertsches, Oliver, and Augustin-Liviu Mare. "Equivariant cohomology of cohomogeneity one actions." Topology and its Applications 167 (April 2014): 36–52. http://dx.doi.org/10.1016/j.topol.2014.03.006.

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20

Vân Lê, Hông. "Compact symplectic manifolds of low cohomogeneity." Journal of Geometry and Physics 25, no. 3-4 (May 1998): 205–26. http://dx.doi.org/10.1016/s0393-0440(97)00018-1.

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21

Conti, Diego. "Cohomogeneity One Einstein-Sasaki 5-Manifolds." Communications in Mathematical Physics 274, no. 3 (July 13, 2007): 751–74. http://dx.doi.org/10.1007/s00220-007-0286-3.

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22

Podest�, Fabio. "Immersions of cohomogeneity one Riemannian manifolds." Monatshefte f�r Mathematik 122, no. 3 (September 1996): 215–25. http://dx.doi.org/10.1007/bf01320185.

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23

ABATE, MARCO, and LAURA GEATTI. "COHOMOGENEITY TWO HYPERBOLIC ACYCLIC STEIN MANIFOLDS." International Journal of Mathematics 03, no. 05 (October 1992): 591–608. http://dx.doi.org/10.1142/s0129167x92000278.

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24

Berndt, Jürgen, José Carlos Díaz-Ramos, and Mohammad Javad Vanaei. "Cohomogeneity one actions on Minkowski spaces." Monatshefte für Mathematik 184, no. 2 (June 18, 2016): 185–200. http://dx.doi.org/10.1007/s00605-016-0945-6.

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25

Dancer, Andrew, and McKenzie Y. Wang. "Kähler-Einstein metrics of cohomogeneity one." Mathematische Annalen 312, no. 3 (November 1, 1998): 503–26. http://dx.doi.org/10.1007/s002080050233.

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26

Gambioli, Andrea. "SU(3)-manifolds of cohomogeneity one." Annals of Global Analysis and Geometry 34, no. 1 (December 13, 2007): 77–100. http://dx.doi.org/10.1007/s10455-007-9097-1.

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27

Dancer, Andrew S., and McKenzie Y. Wang. "On Ricci solitons of cohomogeneity one." Annals of Global Analysis and Geometry 39, no. 3 (October 17, 2010): 259–92. http://dx.doi.org/10.1007/s10455-010-9233-1.

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28

MIRZAIE, R. "ON EUCLIDEAN G-MANIFOLDS WHICH HAVE TWO DIMENSIONAL ORBIT SPACES." International Journal of Mathematics 22, no. 03 (March 2011): 399–406. http://dx.doi.org/10.1142/s0129167x11006829.

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We show that the orbit space of Euclidean space, under the action of a closed and connected Lie group of isometries is homeomorphic to a plane or closed half-plane, if the action is of cohomogeneity two.

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29

Podestà, Fabio. "Cohomogeneity one Riemannian manifolds and Killing fields." Differential Geometry and its Applications 5, no. 4 (December 1995): 311–20. http://dx.doi.org/10.1016/0926-2245(95)00021-6.

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30

Frank, Philipp. "Cohomogeneity one manifolds with positive Euler characteristic." Transformation Groups 18, no. 3 (July 4, 2013): 639–84. http://dx.doi.org/10.1007/s00031-013-9227-8.

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31

Dancer, A., and M. Wang. "Superpotentials and the Cohomogeneity One Einstein Equations." Communications in Mathematical Physics 260, no. 1 (August 2, 2005): 75–115. http://dx.doi.org/10.1007/s00220-005-1410-x.

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32

Searle, Catherine. "Cohomogeneity and positive curvature in low dimensions." Mathematische Zeitschrift 214, no. 1 (September 1993): 491–98. http://dx.doi.org/10.1007/bf02572419.

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33

Grove, Karsten, and Wolfgang Ziller. "Cohomogeneity one manifolds with positive Ricci curvature." Inventiones Mathematicae 149, no. 3 (September 1, 2002): 619–46. http://dx.doi.org/10.1007/s002220200225.

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34

Li, Jifu, Zhiguang Hu, and Shaoqiang Deng. "S-curvature of cohomogeneity one Randers spaces." Journal of Mathematical Analysis and Applications 441, no. 2 (September 2016): 624–34. http://dx.doi.org/10.1016/j.jmaa.2016.03.084.

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35

Bettiol, Renato G., and Paolo Piccione. "Delaunay-Type Hypersurfaces in Cohomogeneity One Manifolds." International Mathematics Research Notices 2016, no. 10 (August 5, 2015): 3124–62. http://dx.doi.org/10.1093/imrn/rnv231.

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36

Gastel, Andreas, and Felix Zorn. "Biharmonic maps of cohomogeneity one between spheres." Journal of Mathematical Analysis and Applications 387, no. 1 (March 2012): 384–99. http://dx.doi.org/10.1016/j.jmaa.2011.09.002.

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37

Searle, Catherine. "Cohomogeneity and positive curvature in low dimensions." Mathematische Zeitschrift 226, no. 1 (September 16, 1997): 165–67. http://dx.doi.org/10.1007/pl00004642.

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38

Schwachhöfer, Lorenz J. "Lower curvature bounds and cohomogeneity one manifolds." Differential Geometry and its Applications 17, no. 2-3 (September 2002): 209–28. http://dx.doi.org/10.1016/s0926-2245(02)00108-0.

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39

Mirzaie, R. "Cohomogeneity Two Actions on Flat Riemannian Manifolds." Acta Mathematica Sinica, English Series 23, no. 9 (June 21, 2007): 1587–92. http://dx.doi.org/10.1007/s10114-007-0952-6.

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40

Püttmann, Thomas, and Anna Siffert. "Harmonic self-maps of cohomogeneity one manifolds." Mathematische Annalen 375, no. 1-2 (July 1, 2019): 247–82. http://dx.doi.org/10.1007/s00208-019-01848-x.

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41

Böhm, Christoph. "Non-existence of cohomogeneity one Einstein metrics." Mathematische Annalen 314, no. 1 (May 1, 1999): 109–25. http://dx.doi.org/10.1007/s002080050288.

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42

Villumsen, Martin. "Cohomogeneity-Three HyperKähler Metrics on Nilpotent Orbits." Annals of Global Analysis and Geometry 28, no. 2 (September 2005): 123–56. http://dx.doi.org/10.1007/s10455-005-6636-5.

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43

HAMBLETON, IAN, and JEAN-CLAUDE HAUSMANN. "EQUIVARIANT PRINCIPAL BUNDLES OVER SPHERES AND COHOMOGENEITY ONE MANIFOLDS." Proceedings of the London Mathematical Society 86, no. 1 (January 2003): 250–72. http://dx.doi.org/10.1112/s0024611502013722.

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We classify smooth ${\rm SO}(n)$-equivariant principal bundles over $S^n$ in terms of their isotropy representations over the north and south poles. This is an example of a general result classifying equivariant $(\Pi, G)$-bundles over manifolds with cohomogeneity 1.2000 Mathematical Subject Classification: 55R91.

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44

Schwachhöfer, Lorenz J., and Kristopher Tapp. "Cohomogeneity one disk bundles with normal homogeneous collars." Proceedings of the London Mathematical Society 99, no. 3 (April 24, 2009): 609–32. http://dx.doi.org/10.1112/plms/pdp012.

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45

MIRZAIE, R. "On negatively curved G-manifolds of low cohomogeneity." Hokkaido Mathematical Journal 38, no. 4 (November 2009): 797–803. http://dx.doi.org/10.14492/hokmj/1258554244.

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46

KIM, CHANG-WAN. "POSITIVELY CURVED MANIFOLDS WITH FIXED POINT COHOMOGENEITY ONE." Communications of the Korean Mathematical Society 21, no. 1 (January 1, 2006): 151–63. http://dx.doi.org/10.4134/ckms.2006.21.1.151.

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47

Abedi, Hosein, and Seyed Mohammad Bagher Kashani. "COHOMOGENEITY ONE RIEMANNIAN MANIFOLDS OF CONSTANT POSITIVE CURVATURE." Journal of the Korean Mathematical Society 44, no. 4 (July 30, 2007): 799–807. http://dx.doi.org/10.4134/jkms.2007.44.4.799.

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48

Console, Sergio, and Carlos Olmos. "Curvature invariants, Killing vector fields, connections and cohomogeneity." Proceedings of the American Mathematical Society 137, no. 03 (October 2, 2008): 1069–72. http://dx.doi.org/10.1090/s0002-9939-08-09669-x.

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49

Chen, Wei, Hong Lü, and Christopher N. Pope. "Separability in cohomogeneity-2 Kerr-NUT-AdS metrics." Journal of High Energy Physics 2006, no. 04 (April 4, 2006): 008. http://dx.doi.org/10.1088/1126-6708/2006/04/008.

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50

Kollross, Andreas. "A classification of hyperpolar and cohomogeneity one actions." Transactions of the American Mathematical Society 354, no. 2 (September 18, 2001): 571–612. http://dx.doi.org/10.1090/s0002-9947-01-02803-3.

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