| Title:
|
Killing Reeb vector fields on some almost contact manifolds (English) |
| Author:
|
Massamba, Fortuné |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0011-4642 |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
151 |
| Issue:
|
3 |
| Year:
|
2026 |
| Pages:
|
407-422 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We discuss the geometric impact of a Killing vector field on certain almost contact manifolds with constant sectional curvatures. We prove that the additional structures given in A. De Nicola, G. Dileo, I. Yudin (2018) can be naturally constructed in the case of nearly Sasakian and nearly cosymplectic manifolds with constant sectional curvatures. (English) |
| Keyword:
|
nearly Sasakian manifold |
| Keyword:
|
nearly cosymplectic manifold |
| Keyword:
|
Killing Reeb vector field |
| MSC:
|
53C15 |
| MSC:
|
53C25 |
| DOI:
|
10.21136/MB.2025.0010-25 |
| . |
| Date available:
|
2026-08-24T07:51:22Z |
| Last updated:
|
2026-08-24 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153714 |
| . |
| Reference:
|
[1] Berestovskii, V. N., Nikonorov, Y. G.: Killing vector fields of constant length on Riemannian manifolds.Sib. Math. J. 49 (2008), 395-407. Zbl 1164.53346, MR 2442533, 10.1007/s11202-008-0039-3 |
| Reference:
|
[2] Blair, D. E.: Riemannian Geometry of Contact and Symplectic Manifolds.Progress in Mathematics 203. Birkhäuser, Boston (2010). Zbl 1246.53001, MR 2682326, 10.1007/978-0-8176-4959-3 |
| Reference:
|
[3] Blair, D. E., Showers, D. K., Yano, K.: Nearly Sasakian structures.Kodai Math. Semin. Rep. 27 (1976), 175-180. Zbl 0328.53036, MR 0405287, 10.2996/kmj/1138847173 |
| Reference:
|
[4] Cappelletti-Montano, B., Nicola, A. De, Dileo, G., Yudin, I.: Nearly Sasakian manifolds revisited.Complex Manifolds 6 (2019), 320-334. Zbl 1427.53052, MR 3987860, 10.1515/coma-2019-0017 |
| Reference:
|
[5] Cappelletti-Montano, B., Dileo, G.: Nearly Sasakian geometry and $SU(2)$-structures.Ann. Mat. Pura Appl. (4) 195 (2016), 897-922. Zbl 1406.53028, MR 3500312, 10.1007/s10231-015-0496-9 |
| Reference:
|
[6] Nicola, A. De, Dileo, G., Yudin, I.: On nearly Sasakian and nearly cosymplectic manifolds.Ann. Mat. Pura Appl. (4) 197 (2018), 127-138. Zbl 1384.53028, MR 3747524, 10.1007/s10231-017-0671-2 |
| Reference:
|
[7] Deshmukh, S., Al-Dayel, I.: A note on nearly Sasakian and nearly cosymplictic structures of 5-dimensional spheres.Int. Electron. J. Geom. 11 (2018), 90-95. Zbl 1409.53042, MR 3875263, 10.36890/iejg.545110 |
| Reference:
|
[8] Deshmukh, S., Belova, O.: On killing vector fields on Riemannian manifolds.Mathematics 2021 (2021), Article ID 259, 17 pages. 10.3390/math9030259 |
| Reference:
|
[9] Martelli, D., Sparks, J.: Toric geometry, Sasaki-Einstein manifolds and a new infinite class of AdS/CFT duals.Commun. Math. Phys. 262 (2006), 51-89. Zbl 1112.53034, MR 2200882, 10.1007/s00220-005-1425-3 |
| Reference:
|
[10] Massamba, F., Nzunogera, A.: A note on nearly Sasakian manifolds.Mathematics 2023 (2023), Article ID 2634, 20 pages. 10.3390/math11122634 |
| Reference:
|
[11] Olszak, Z.: Five-dimensional nearly Sasakian manifolds.Tensor, New Ser. 34 (1980), 273-276. Zbl 0448.53036, MR 0597312 |
| Reference:
|
[12] O'Neill, B.: Semi-Riemannian Geometry: With Applications to Relativity.Pure and Applied Mathematics 103. Academic Press, London (1983). Zbl 0531.53051, MR 1567613 |
| Reference:
|
[13] Rong, X.: Positive curvature, local and global symmetry, and fundamental groups.Am. J. Math. 121 (1999), 931-943. Zbl 0978.53073, MR 1713297, 10.1353/ajm.1999.0036 |
| Reference:
|
[14] Shore, S. N.: Astrophysical Hydrodynamics: An Introduction.Wiley, Weinheim (2007). 10.1002/9783527619054 |
| Reference:
|
[15] Wolf, J. A.: Spaces of Constant Curvature.AMS, Providence (2011). Zbl 1216.53003, MR 2742530, 10.1090/chel/372 |
| . |
