Browse > Article
http://dx.doi.org/10.4134/JKMS.2005.42.5.913

PSEUDO-SYMMETRIC CONTACT 3-MANIFOLDS  

CHO, JONG TAEK (Department of Mathematics, Chonnam National University)
INOGUCHI, JUN-ICHI (Department of Mathematics Education Facylty of Education Utsunomiya University)
Publication Information
Journal of the Korean Mathematical Society / v.42, no.5, 2005 , pp. 913-932 More about this Journal
Abstract
Contact Homogeneous 3-manifolds are pseudo-symmetric spaces of constant type. All Sasakian 3-manifolds are pseudo-symmetric spaces of constant type.
Keywords
pseudo-symmetric spaces; contact Riemannian 3-manifolds.;
Citations & Related Records

Times Cited By Web Of Science : 7  (Related Records In Web of Science)
Times Cited By SCOPUS : 4
연도 인용수 순위
1 D. E. Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Math. 509 (1976), Springer-Verlag, Berlin-Heidelberg-New-York
2 D. E. Blair, Th. Koufogiorgos and B. J. Papantoniou, Contact metric manifolds satisfying a nullity condition, Israel J. Math. 91 (1995), 189-214   DOI
3 D. E. Blair, Th. Koufogiorgos, and R. Sharma, A classification of 3-dimensional contact metric manifolds with $Q{\varphi}={\varphi}Q$, Kodai Math. J. 13 (1990), 391-401   DOI
4 D. E. Blair and R. Sharma, Three-dimensional locally symmetric contact metric manifolds, Boll. Unione. Mat. Ital. Sez. A Mat. Soc. Cult. (8) 4 (1990), no. 3, 385-390
5 L. Bianchi, Lezioni di Geometrie Differenziale, E. Spoerri Librao-Editore, 1894
6 J. Inoguchi, Minimal surfaces in 3-dimensional solvable Lie groups, Chinese Ann. Math. Ser. B 24 (2003), 73-84   DOI   ScienceOn
7 J. Inoguchi, T. Kumamoto, N. Ohsugi, and Y. Suyama, Differential geometry of curves and surfaces in 3-dimensional homogeneous spaces III, Fukuoka Univ. Sci. Rep. 30 (2000), 131-160
8 O. Kowalski, Spaces with volume preserving symmetries and related classes of Riemannian manifolds, Rend. Sem. Mat. Univ. Politec. Torino 64 (1983), 131- 159
9 O. Kowalski and M. Sekizawa, Local isometry classes of Riemannian 3-manifolds with constant Ricci eigenvalues ${\rho}_1={\rho}_2{\neq}{\rho}_3$ Arch. Math. (Brno) 32 (1996), 137-145
10 O. Kowalski, A classification of Riemannian 3-manifolds with constant principal Ricci curvatures ${\rho}_1={\rho}_2{\neq}{\rho}_3$, Nagoya Math. J. 132 (1993), 1-36   DOI
11 S. Tanno, Variational problems on contact Riemannian manifolds, Trans. Amer. Math. Soc. 314 (1989), 349-379   DOI   ScienceOn
12 W. M. Thurston, Three-dimensional Geometry and Topology I, Princeton Math.Ser., vol. 35 (S. Levy, eds.), 1997
13 F. Tricerri and L. Vanhecke, Homogeneous Structures on Riemannian Mani- folds, London Math. Soc. Lecture Note Ser. vol. 83, Cambridge Univ. Press, London, 1983
14 S. S. Chern and R. S. Hamilton, On Riemannian metrics adapted to three-dimensional contact manifolds, Lecture Notes in Math. 1111 (1985), Springer Verlag, 279-305
15 D. E. Blair and L. Vanhecke, Symmetries and ${\varphi}-symmetric$spaces, Tohoku Math. J. 39 (1987), no. 2, 373-383   DOI
16 G. Calvaruso, D. Perrone, and L. Vanhecke, Homogeneity on three-dimensional contact metric manifolds , Israel J. Math. 114 (1999), 301-321   DOI
17 E. Cartan, Lecon sur la geometrie des espaces de Riemann, Second Edition, Gauthier-Villards, Paris, 1946
18 J. T. Cho, A class of contact Riemannian manifolds whose associated CR-structure are integrable, Publ. Math. Debrecen 63 (2003), 193-211
19 J. T. Cho and L. Vanhecke, Classification of symmetric-like contact metric $({\kappa},{\mu})$ spaces, Publ. Math. Debrecen 62 (2003), 337-349
20 J. Deprez, R. Deszcz, and L. Verstraelen, Examples of pseudo-symmetric conformally flat warped products, Chinese J. Math. 17 (1989), 51-65
21 R. Deszcz, On pseudosymmetric spaces, Bull. Soc. Math. Belg. 44 (1992), 1-34
22 Y. Eliashberg and W. Thurston, Confoliations, AMS University Lecture Series 13 (1998)
23 N. Hashimoto and M. Sekizawa, Three-dimensional conformally flat pseudo-symmetric spaces of constant type, Arch. Math. (Brno) 36 (2000), 279-286
24 J. Milnor, Curvature of left invariant metrics on Lie groups, Adv. Math. 21 (1976), 293-329   DOI
25 O. Kowalski and M. Sekizawa, Three-dimensional Riemannian manifolds of c-conullity two, Riemann-ian Manifolds of Conullity Two, Chapter 11, World Scientific, Singapore, 1996
26 O. Kowalski and M. Sekizawa, Pseudo-symmetric spaces of constant type in dimension three-elliptic spaces, Rend. Mat. Appl. (7) 17 (1997), 477-512
27 O. Kowalski and M. Sekizawa, Pseudo-symmetric spaces of constant type in dimension three-non-elliptic spaces, Bull. Tokyo Gakugei Univ. (4) 50 (1998), 1-28
28 B. O'Neill, Semi-Riemannian Geometry with Application to Relativity, Academic Press, Orland, 1983
29 V. Patrangenaru, Classifying 3- and 4-dimensional homogeneous Riemannian manifolds by Cartan triples , Pacific J. Math. 173 (1996), 511-532   DOI
30 D. Perrone, Homogeneous contact Riemannian three-manifolds, Illinois J. Math. 13 (1997), 243-256
31 T. Takahashi, Sasakian manifolds with pseudo-Riemannian metric, Tohoku Math. J. 21 (1969), 271-290   DOI
32 S. Tanno, Sur une variete de K-contact metrique de dimension 3, C. R. Math. Acad. Sci. Paris 263 (1966), A 317-A319
33 S. Tanno, Locally symmetric K-contact Riemannian manifolds, Proc. Japan Acad. Ser. A Math. Sci. 43 (1967), 581-583