Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/conformally-flat-almost-kenmotsu-3-manifolds-wNAtaMVO3n
References (27)
-
K Kenmotsu (1972)
A class of almost contact Riemannian manifoldsTôhoku Math. J., 24
-
K. Kenmotsu (1972)
A CLASS OF ALMOST CONTACT RIEMANNIAN MANIFOLDSTohoku Mathematical Journal, 24
-
(2007)
Geometry of Kenmotsu Manifolds. Publishing House of Transilvania University of Braşov, Braşov -
Y Wang (2016)
Conformally flat CR-integrable almost Kenmotsu manifoldsBull. Math. Soc. Sci. Math. Roumanie, 59
-
Yaning Wang (2016)
Three-dimensional locally symmetric almost Kenmotsu manifoldsAnnales Polonici Mathematici, 116
-
A. Pastore, Vincenzo Saltarelli (2011)
GENERALIZED NULLITY DISTRIBUTIONS ON ALMOST KENMOTSU MANIFOLDS -
D. Blair, H. Yildirim (2016)
On Conformally Flat Almost Contact Metric ManifoldsMediterranean Journal of Mathematics, 13
-
D. Janssens, L. Vanhecke (1981)
Almost contact structures and curvature tensorsKodai Mathematical Journal, 4
-
J. Milnor (1976)
Curvatures of left invariant metrics on lie groupsAdvances in Mathematics, 21
-
SV Kharitonova (2011)
Almost $$C(\lambda )$$ C ( λ ) -manifoldsJ. Math. Sci., 177
-
S. Kharitonova (2011)
Almost C(λ)-manifoldsJournal of Mathematical Sciences, 177
-
Vincenzo Saltarelli (2010)
Three-Dimensional Almost Kenmotsu Manifolds Satisfying Certain Nullity ConditionsBulletin of the Malaysian Mathematical Sciences Society, 38
-
G Dileo, AM Pastore (2009)
Almost Kenmotsu manifolds with a condition of $$\eta $$ η -parallelismDiffer. Geom. Appl., 27
-
JT Cho (2016)
Conformally flat normal almost contact metric 3-manifoldsHonam Math. J., 38
-
T. Binh, L. Tamâssy, U. De, M. Tarafdar (2002)
Some remarks on almost Kenmotsu manifolds.Mathematica Pannonica, 13
-
Y Wang (2016)
A class of $$3$$ 3 -dimensional almost Kenmotsu manifolds with harmonic curvature tensorsOpen Math., 14
-
G. Dileo, A. Pastore (2009)
Almost Kenmotsu Manifolds and Nullity DistributionsJournal of Geometry, 93
-
C. Özgür, U. De (2006)
On the quasi-conformal curvature tensor of a Kenmotsu manifold.Mathematica Pannonica, 17
-
G. Dileo, A. Pastore (2009)
Almost Kenmotsu manifolds with a condition of η-parallelismDifferential Geometry and Its Applications, 27
-
D. Perrone (2013)
Almost contact metric manifolds whose Reeb vector field is a harmonic sectionActa Mathematica Hungarica, 138
-
D. Blair (2002)
Riemannian Geometry of Contact and Symplectic Manifolds -
G. Dileo, A. Pastore (2007)
Almost Kenmotsu manifolds and local symmetryBulletin of The Belgian Mathematical Society-simon Stevin, 14
-
JT Cho (2014)
Notes on almost Kenmotsu 3-manifoldsHonam Math. J., 36
-
Jong Cho (2016)
Local symmetry on almost Kenmotsu three-manifoldsHokkaido Mathematical Journal, 45
-
G Pitiş (2007)
Geometry of Kenmotsu Manifolds -
Jong Cho, M. Kimura (2014)
Reeb flow symmetry on almost contact three-manifoldsDifferential Geometry and Its Applications, 35
-
Yaning Wang (2016)
A class of 3-dimensional almost Kenmotsu manifolds with harmonic curvature tensorsOpen Mathematics, 14
- Publisher
- Springer Journals
- Copyright
- Copyright © 2017 by Springer International Publishing AG
- Subject
- Mathematics; Mathematics, general
- ISSN
- 1660-5446
- eISSN
- 1660-5454
- DOI
- 10.1007/s00009-017-0984-9
- Publisher site
- See Article on Publisher Site
Abstract
In this paper, by virtue of a system of partial differential equations, we give a necessary and sufficient condition for an almost Kenmotsu 3-manifold to be conformally flat. As an application, we obtain that an almost Kenmotsu 3-H-manifold with scalar curvature invariant along the Reeb vector field is conformally flat if and only if it is locally isometric to either the hyperbolic space $$\mathbb {H}^3(-1)$$ H 3 ( - 1 ) or the Riemannian product $$\mathbb {H}^{2}(-4)\times \mathbb {R}$$ H 2 ( - 4 ) × R . Some concrete examples verifying main results are presented.
Journal
Mediterranean Journal of Mathematics – Springer Journals
Published: Aug 14, 2017