| Title:
|
H-conformal anti-invariant submersions from almost quaternionic Hermitian manifolds (English) |
| Author:
|
Park, Kwang Soon |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
70 |
| Issue:
|
3 |
| Year:
|
2020 |
| Pages:
|
631-656 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We introduce the notions of h-conformal anti-invariant submersions and h-conformal Lagrangian submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds as a generalization of Riemannian submersions, horizontally conformal submersions, anti-invariant submersions, h-anti-invariant submersions, h-Lagrangian submersion, conformal anti-invariant submersions. We investigate their properties: the integrability of distributions, the geometry of foliations, the conditions for such maps to be totally geodesic, etc. Finally, we give some examples of such maps. (English) |
| Keyword:
|
horizontally conformal submersion |
| Keyword:
|
quaternionic manifold |
| Keyword:
|
totally geodesic |
| MSC:
|
53C15 |
| MSC:
|
53C26 |
| MSC:
|
53C43 |
| idZBL:
|
07250680 |
| idMR:
|
MR4151696 |
| DOI:
|
10.21136/CMJ.2020.0264-18 |
| . |
| Date available:
|
2020-09-07T09:34:29Z |
| Last updated:
|
2022-10-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148319 |
| . |
| Reference:
|
[1] Akyol, M. A., Şahin, B.: Conformal anti-invariant submersions from almost Hermitian manifolds.Turk. J. Math. 40 (2016), 43-70. Zbl 1424.53056, MR 3438784, 10.3906/mat-1408-20 |
| Reference:
|
[2] Alekseevsky, D. V., Marchiafava, S.: Almost complex submanifolds of quaternionic manifolds.Steps in Differential Geometry Institute of Mathematics and Informatics, University of Debrecen, Debrecen (2001), 23-38. Zbl 1037.53029, MR 1859285 |
| Reference:
|
[3] Baird, P., Wood, J. C.: Harmonic Morphisms between Riemannian Manifolds.London Mathematical Society Monographs. New Series 29. Oxford University Press, Oxford (2003). Zbl 1055.53049, MR 2044031, 10.1093/acprof:oso/9780198503620.001.0001 |
| Reference:
|
[4] Besse, A. L.: Einstein Manifolds.Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge 10. Springer, Berlin (1987). Zbl 0613.53001, MR 0867684, 10.1007/978-3-540-74311-8 |
| Reference:
|
[5] Bourguignon, J.-P.: A mathematician's visit to Kaluza-Klein theory.Rend. Semin. Mat., Torino Special Issue (1989), 143-163. Zbl 0717.53062, MR 1086213 |
| Reference:
|
[6] J.-P. Bourguignon, H. B. Lawson, Jr.: Stability and isolation phenomena for Yang-Mills fields.Commum. Math. Phys. 79 (1981), 189-230. Zbl 0475.53060, MR 0612248, 10.1007/BF01942061 |
| Reference:
|
[7] Chen, B.-Y.: Geometry of Slant Submanifolds.Katholieke Universiteit Leuven, Leuven (1990). Zbl 0716.53006, MR 1099374 |
| Reference:
|
[8] Cortés, V., Mayer, C., Mohaupt, T., Saueressig, F.: Special geometry of Euclidean supersymmetry. I. Vector multiplets.J. High Energy Phys. 2004 (2004), Article ID 028, 73 pages. MR 2061551, 10.1088/1126-6708/2004/03/028 |
| Reference:
|
[9] Falcitelli, M., Ianus, S., Pastore, A. M.: Riemannian Submersions and Related Topics.World Scientific, River Edge (2004). Zbl 1067.53016, MR 2110043, 10.1142/5568 |
| Reference:
|
[10] Fuglede, B.: Harmonic morphisms between Riemannian manifolds.Ann. Inst. Fourier 28 (1978), 107-144. Zbl 0339.53026, MR 0499588, 10.5802/aif.691 |
| Reference:
|
[11] Gray, A.: Pseudo-Riemannian almost product manifolds and submersions.J. Math. Mech. 16 (1967), 715-737. Zbl 0147.21201, MR 0205184, 10.1512/iumj.1967.16.16047 |
| Reference:
|
[12] Gudmundsson, S.: The Geometry of Harmonic Morphisms. Ph.D. Thesis.University of Leeds, Leeds (1992), Available at http://www.matematik.lu.se/matematiklu/personal/sigma/Doctoral-thesis.pdf. MR 1068448 |
| Reference:
|
[13] Gudmundsson, S., Wood, J. C.: Harmonic morphisms between almost Hermitian manifolds.Boll. Unione Mat. Ital., VII. Ser., B 11 (1997), 185-197. Zbl 0879.53023, MR 1456260 |
| Reference:
|
[14] Ianuş, S., Mazzocco, R., Vîlcu, G. E.: Riemannian submersions from quaternionic manifolds.Acta. Appl. Math. 104 (2008), 83-89. Zbl 1151.53329, MR 2434668, 10.1007/s10440-008-9241-3 |
| Reference:
|
[15] Ianuş, S., Vişinescu, M.: Kaluza-Klein theory with scalar fields and generalized Hopf manifolds.Classical Quantum Gravity 4 (1987), 1317-1325. Zbl 0629.53072, MR 0905571, 10.1088/0264-9381/4/5/026 |
| Reference:
|
[16] Ianuş, S., Vişinescu, M.: Space-time compactification and Riemannian submersions.The Mathematical Heritage of C. F. Gauss World Scientific, River Edge (1991), 358-371. Zbl 0765.53064, MR 1146240, 10.1142/9789814503457_0026 |
| Reference:
|
[17] Ishihara, T.: A mapping of Riemannian manifolds which preserves harmonic functions.J. Math. Kyoto Univ. 19 (1979), 215-229. Zbl 0421.31006, MR 0545705, 10.1215/kjm/1250522428 |
| Reference:
|
[18] Jin, D. H., Lee, J. W.: Conformal anti-invariant submersions from hyper-Kähler manifolds.JP J. Geom. Topol. 19 (2016), 161-183. Zbl 1358.53051, 10.17654/GT019020161 |
| Reference:
|
[19] Mustafa, M. T.: Applications of harmonic morphisms to gravity.J. Math. Phys. 41 (2000), 6918-6929. Zbl 0974.58017, MR 1781415, 10.1063/1.1290381 |
| Reference:
|
[20] O'Neill, B.: The fundamental equations of a submersion.Mich. Math. J. 13 (1966), 459-469. Zbl 0145.18602, MR 0200865, 10.1307/mmj/1028999604 |
| Reference:
|
[21] Park, K.-S.: H-semi-invariant submersions.Taiwanese J. Math. 16 (2012), 1865-1878. Zbl 1262.53028, MR 2970690, 10.11650/twjm/1500406802 |
| Reference:
|
[22] Park, K.-S.: Almost h-conformal semi-invariant submersions from almost quaternionic Hermitian manifolds.(to appear) in Hacet. J. Math. Stat. MR 3284038, 10.15672/hujms.599132 |
| Reference:
|
[23] Park, K.-S.: H-anti-invariant submersions from almost quaternionic Hermitian manifolds.Czech. Math. J. 67 (2017), 557-578. Zbl 06738539, MR 3661061, 10.21136/CMJ.2017.0143-16 |
| Reference:
|
[24] Park, K.-S., Prasad, R.: Semi-slant submersions.Bull. Korean Math. Soc. 50 (2013), 951-962. Zbl 1273.53023, MR 3066240, 10.4134/BKMS.2013.50.3.951 |
| Reference:
|
[25] Ponge, R., Reckziegel, H.: Twisted products in pseudo-Riemannian geometry.Geom. Dedicata 48 (1993), 15-25. Zbl 0792.53026, MR 1245571, 10.1007/BF01265674 |
| Reference:
|
[26] Şahin, B.: Anti-invariant Riemannian submersions from almost Hermitian manifolds.Cent. Eur. J. Math. 8 (2010), 437-447. Zbl 1207.53036, MR 2653653, 10.2478/s11533-010-0023-6 |
| Reference:
|
[27] Şahin, B.: Slant submersions from almost Hermitian manifolds.Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 54 (2011), 93-105. Zbl 1224.53054, MR 2799245 |
| Reference:
|
[28] Şahin, B.: Riemannian submersions from almost Hermitian manifolds.Taiwanese J. Math. 17 (2013), 629-659. Zbl 1286.53041, MR 3044527, 10.11650/tjm.17.2013.2191 |
| Reference:
|
[29] Şahin, B.: Semi-invariant submersions from almost Hermitian manifolds.Can. Math. Bull. 56 (2013), 173-183. Zbl 1259.53014, MR 3009415, 10.4153/CMB-2011-144-8 |
| Reference:
|
[30] Urakawa, H.: Calculus of Variations and Harmonic Maps.Translations of Mathematical Monographs 132. American Mathematical Society, Providence (1993). Zbl 0799.58001, MR 1252178, 10.1090/mmono/132 |
| Reference:
|
[31] Watson, B.: Almost Hermitian submersions.J. Differ. Geom. 11 (1976), 147-165. Zbl 0355.53037, MR 0407784, 10.4310/jdg/1214433303 |
| Reference:
|
[32] Watson, B.: $G,G'$-Riemannian submersions and nonlinear gauge field equations of general relativity.Global Analysis - Analysis on Manifolds Teubner Texts in Mathematics 57. Teubner, Leipzig (1983), 324-349. Zbl 0525.53052, MR 0730623 |
| . |
