# Conformally Flat Almost Kenmotsu 3-Manifolds

Conformally Flat Almost Kenmotsu 3-Manifolds 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mediterranean Journal of Mathematics Springer Journals

# Conformally Flat Almost Kenmotsu 3-Manifolds

, Volume 14 (5) – Aug 14, 2017
16 pages

/lp/springer_journal/conformally-flat-almost-kenmotsu-3-manifolds-wNAtaMVO3n
Publisher
Springer International Publishing
Subject
Mathematics; Mathematics, general
ISSN
1660-5446
eISSN
1660-5454
D.O.I.
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 MathematicsSpringer Journals

Published: Aug 14, 2017

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