| Title:
|
On quasirecurrent manifolds (English) |
| Author:
|
Kim, Jaeman |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
150 |
| Issue:
|
3 |
| Year:
|
2025 |
| Pages:
|
405-413 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We introduce a type of Riemannian manifolds (namely, quasirecurrent manifold) and study its several geometric properties. Among others, we prove that the scalar curvature of such a manifold is constant, and that the manifold is Einstein under certain condition. In addition, we deal with a quasirecurrent product manifold. Finally, we ensure the existence of quasirecurrent manifold by a proper example. (English) |
| Keyword:
|
quasirecurrent manifold |
| Keyword:
|
associated vector field |
| Keyword:
|
constant scalar curvature |
| Keyword:
|
Ricci symmetry |
| Keyword:
|
Einstein |
| Keyword:
|
cyclic Ricci symmetry |
| Keyword:
|
conformally flat |
| Keyword:
|
quasirecurrent product manifold |
| Keyword:
|
space of constant curvature |
| MSC:
|
53A55 |
| MSC:
|
53B20 |
| DOI:
|
10.21136/MB.2024.0038-24 |
| . |
| Date available:
|
2025-09-26T14:35:08Z |
| Last updated:
|
2025-09-26 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153084 |
| . |
| Reference:
|
[1] Adati, T., Miyazawa, T.: On a Riemannian space with recurrent conformal curvature.Tensor, New Ser. 18 (1967), 348-354. Zbl 0152.39103, MR 0215251 |
| 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:
|
[7] Pokhariyal, G. P., Moindi, S. K., Nzimbi, B. M.: $W_2$-recurrent LP-Sasakian manifold.Univers. J. Math. Math. Sci. 3 (2013), 119-128. Zbl 1278.53034 |
| Reference:
|
[8] Ruse, H. S.: On simply harmonic spaces.J. Lond. Math. Soc. 21 (1946), 243-247. Zbl 0063.06626, MR 0021708, 10.1112/jlms/s1-21.4.243 |
| Reference:
|
[9] Ruse, H. S.: On simply harmonic "kappa spaces" of four dimensions.Proc. Lond. Math. Soc., II. Ser. 50 (1948), 317-329. Zbl 0030.37202, MR 0027170, 10.1112/plms/s2-50.4.317 |
| Reference:
|
[10] Ruse, H. S.: Three-dimensional spaces of recurrent curvature.Proc. Lond. Math. Soc., II. Ser. 50 (1948), 438-446. Zbl 0038.34303, MR 0029250, 10.1112/plms/s2-50.6.438 |
| Reference:
|
[11] Walker, A. G.: On Ruse's spaces of recurrent curvature.Proc. Lond. Math. Soc., II. Ser. 52 (1950), 36-64. Zbl 0039.17702, MR 0037574, 10.1112/plms/s2-52.1.36 |
| . |
