| Title:
|
Curvature tensors and Ricci solitons with respect to Zamkovoy connection in anti-invariant submanifolds of trans-Sasakian manifold (English) |
| Author:
|
Karmakar, Payel |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
147 |
| Issue:
|
3 |
| Year:
|
2022 |
| Pages:
|
419-434 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The present paper deals with the study of some properties of anti-invariant submanifolds of trans-Sasakian manifold with respect to a new non-metric affine connection called Zamkovoy connection. The nature of Ricci flat, concircularly flat, $\xi $-projectively flat, $M$-projectively flat, $\xi $-$M$-projectively flat, pseudo projectively flat and $\xi $-pseudo projectively flat anti-invariant submanifolds of trans-Sasakian manifold admitting Zamkovoy connection are discussed. Moreover, Ricci solitons on Ricci flat, concircularly flat, $M$-projectively flat and pseudo projectively flat anti-invariant submanifolds of trans-Sasakian manifold admitting the aforesaid connection are studied. At last, some conclusions are made after observing all the results and an example of an anti-invariant submanifold of a trans-Sasakian manifold is given in which all the results can be verified easily. (English) |
| Keyword:
|
anti-invariant submanifold |
| Keyword:
|
trans-Sasakian manifold |
| Keyword:
|
Zamkovoy connection |
| Keyword:
|
$\eta $-Einstein manifold |
| Keyword:
|
Ricci curvature tensor |
| Keyword:
|
concircular curvature tensor |
| Keyword:
|
projective curvature tensor |
| Keyword:
|
$M$-projective curvature tensor |
| Keyword:
|
pseudo projective curvature tensor |
| Keyword:
|
Ricci soliton\looseness -1 |
| MSC:
|
53C05 |
| MSC:
|
53C15 |
| MSC:
|
53C20 |
| MSC:
|
53C25 |
| MSC:
|
53C40 |
| idZBL:
|
Zbl 07584134 |
| idMR:
|
MR4482315 |
| DOI:
|
10.21136/MB.2021.0058-21 |
| . |
| Date available:
|
2022-09-05T09:42:09Z |
| Last updated:
|
2022-12-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151017 |
| . |
| Reference:
|
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