| Title:
|
Some type of semisymmetry on two classes of almost Kenmotsu manifolds (English) |
| Author:
|
Dey, Dibakar |
| Author:
|
Majhi, Pradip |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 (print) |
| ISSN:
|
2336-1298 (online) |
| Volume:
|
29 |
| Issue:
|
3 |
| Year:
|
2021 |
| Pages:
|
457-471 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $(k,\mu )'$-almost Kenmotsu manifold satisfying $Q\cdot R = 0$ is locally isometric to $\mathbb {H}^{n+1}(-4) \times \mathbb {R}^n$ and a $(k,\mu )'$\HH 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. (English) |
| Keyword:
|
Almost Kenmotsu manifolds |
| Keyword:
|
Semisymmetry |
| Keyword:
|
Pseudosymmetry |
| Keyword:
|
Hyperbolic space. |
| MSC:
|
53C25 |
| MSC:
|
53D15 |
| idZBL:
|
Zbl 07484380 |
| idMR:
|
MR4355422 |
| . |
| Date available:
|
2022-01-10T10:08:10Z |
| Last updated:
|
2022-04-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149329 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
