Browse > Article
http://dx.doi.org/10.4134/BKMS.b150772

A NOTE ON ALMOST CONTACT RIEMANNIAN 3-MANIFOLDS II  

Inoguchi, Jun-ichi (Institute of Mathematics University of Tsukuba)
Publication Information
Bulletin of the Korean Mathematical Society / v.54, no.1, 2017 , pp. 85-97 More about this Journal
Abstract
We classify Kenmotsu 3-manifolds and cosymplectic 3-manifolds with ${\eta}-parallel$ Ricci operator.
Keywords
cosymplectic 3-manifolds; Kenmotsu 3-manifolds; Sasakian 3-manifolds; ${\eta}-parallelism$; strong ${\eta}-parallelism$;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 M. Kon, Invariant submanifolds in Sasakian manifolds, Math. Ann. 219 (1976), no. 3, 277-290.   DOI
2 Z. Olszak, Normal almost contact metric manifolds of dimension three, Ann. Polon. Math. 47 (1986), 42-50.
3 B. O'Neill, Semi-Riemannian Geometry with Application to Relativity, Academic Press, Orland, 1983.
4 K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J. 24 (1972), 93-103.   DOI
5 M. Kimura and S. Maeda, On real hypersurfaces of a complex projective space, Math. Z. 202 (1989), no. 3, 299-311.   DOI
6 M. Belkhelfa, F. Dillen, and J. Inoguchi, Surfaces with parallel second fundamental form in Bianchi-Cartan-Vranceanu spaces, in: PDE's, Submanifolds and Affine Differential Geometry (Warsaw, 2000), pp. 67-87, Banach Center Publ. 57, Polish Acad. Sci., Warsaw, 2002.
7 D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Progress in Mathematics, 203, Birkhauser Boston, Inc., Boston, 2002.
8 D. E. Blair and J. A. Oubina, Conformal and related changes of metric on the product of two almost contact metric manifolds, Publ. Math. 34 (1990), no. 1, 199-207.   DOI
9 D. E. Blair and L. Vanhecke, Symmetries and ${\varphi}$-symmetric spaces, Tohoku Math. J. 39 (1987), no. 3, 373-383.   DOI
10 J. T. Cho, Local symmetry on almost Kenmotsu three-manifolds, Hokkaido Math. J. 45 (2016), no. 3, 435-442.   DOI
11 J. Inoguchi, A note on almost contact Riemannian 3-manifolds, Bull. Yamagata Univ. Natur. Sci. 17 (2010), no. 1, 1-6.
12 J. T. Cho and M. Kimura, Reeb flow symmetry on almost contact three-manifolds, Differential Geom. Appl. 35 (2014), 266-273.   DOI
13 U. C. De, On ${\Phi}$-symmetric Kenmotsu manifolds, Int. Electron. J. Geom. 1 (2008), no. 1, 33-38.
14 U. C. De and G. Pathak, On 3-dimensional Kenmotsu manifolds, Indian J. Pure Appl. Math. 35 (2004), no. 2, 159-165.
15 J.-B. Jun, U. C. De, and G. Pathak, On Kenmotsu manifolds, J. Korean Math. Soc. 42 (2005), no. 3, 435-445.   DOI