Some type of semisymmetry on two classes of almost Kenmotsu manifolds

Dey, Dibakar, and Majhi, Pradip. "Some type of semisymmetry on two classes of almost Kenmotsu manifolds." Communications in Mathematics 29.3 (2021): 457-471. <http://eudml.org/doc/297767>.

@article{Dey2021,
abstract = {The object of the present paper is to study some types of semisymmetry conditions on two classes of almost Kenmotsu manifolds. It is shown that a $(k,\mu )$-almost Kenmotsu manifold satisfying the curvature condition $Q\cdot R = 0$ is locally isometric to the hyperbolic space $\mathbb \{H\}^\{2n+1\}(-1)$. Also in $(k,\mu )$-almost Kenmotsu manifolds the following conditions: (1) local symmetry $(\nabla R = 0)$, (2) semisymmetry $(R\cdot R = 0)$, (3) $Q(S,R) = 0$, (4) $R\cdot R = Q(S,R)$, (5) locally isometric to the hyperbolic space $\mathbb \{H\}^\{2n+1\}(-1)$ are equivalent. Further, it is proved that a $(k,\mu )^\{\prime \}$-almost Kenmotsu manifold satisfying $Q\cdot R = 0$ is locally isometric to $\mathbb \{H\}^\{n+1\}(-4) \times \mathbb \{R\}^n$ and a $(k,\mu )^\{\prime \}$almost Kenmotsu manifold satisfying any one of the curvature conditions $Q(S,R) = 0$ or $R\cdot R = Q(S,R)$ is either an Einstein manifold or locally isometric to $\mathbb \{H\}^\{n+1\}(-4) \times \mathbb \{R\}^n$. Finally, an illustrative example is presented.},
author = {Dey, Dibakar, Majhi, Pradip},
journal = {Communications in Mathematics},
keywords = {Almost Kenmotsu manifolds; Semisymmetry; Pseudosymmetry; Hyperbolic space},
language = {eng},
number = {3},
pages = {457-471},
publisher = {University of Ostrava},
title = {Some type of semisymmetry on two classes of almost Kenmotsu manifolds},
url = {http://eudml.org/doc/297767},
volume = {29},
year = {2021},
}

TY - JOUR
AU - Dey, Dibakar
AU - Majhi, Pradip
TI - Some type of semisymmetry on two classes of almost Kenmotsu manifolds
JO - Communications in Mathematics
PY - 2021
PB - University of Ostrava
VL - 29
IS - 3
SP - 457
EP - 471
AB - The object of the present paper is to study some types of semisymmetry conditions on two classes of almost Kenmotsu manifolds. It is shown that a $(k,\mu )$-almost Kenmotsu manifold satisfying the curvature condition $Q\cdot R = 0$ is locally isometric to the hyperbolic space $\mathbb {H}^{2n+1}(-1)$. Also in $(k,\mu )$-almost Kenmotsu manifolds the following conditions: (1) local symmetry $(\nabla R = 0)$, (2) semisymmetry $(R\cdot R = 0)$, (3) $Q(S,R) = 0$, (4) $R\cdot R = Q(S,R)$, (5) locally isometric to the hyperbolic space $\mathbb {H}^{2n+1}(-1)$ are equivalent. Further, it is proved that a $(k,\mu )^{\prime }$-almost Kenmotsu manifold satisfying $Q\cdot R = 0$ is locally isometric to $\mathbb {H}^{n+1}(-4) \times \mathbb {R}^n$ and a $(k,\mu )^{\prime }$almost Kenmotsu manifold satisfying any one of the curvature conditions $Q(S,R) = 0$ or $R\cdot R = Q(S,R)$ is either an Einstein manifold or locally isometric to $\mathbb {H}^{n+1}(-4) \times \mathbb {R}^n$. Finally, an illustrative example is presented.
LA - eng
KW - Almost Kenmotsu manifolds; Semisymmetry; Pseudosymmetry; Hyperbolic space
UR - http://eudml.org/doc/297767
ER -