| Title:
|
Some constructions of biharmonic maps on the warped product manifolds (English) |
| Author:
|
Bennouar, Abdelmadjid |
| Author:
|
Ouakkas, Seddik |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
58 |
| Issue:
|
4 |
| Year:
|
2017 |
| Pages:
|
481-500 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we characterize a class of biharmonic maps from and between product manifolds in terms of the warping function. Examples are constructed when one of the factors is either Euclidean space or sphere. (English) |
| Keyword:
|
harmonic map |
| Keyword:
|
biharmonic map |
| Keyword:
|
warped product |
| MSC:
|
31B30 |
| MSC:
|
53C25 |
| MSC:
|
58E20 |
| MSC:
|
58E30 |
| idZBL:
|
Zbl 06837081 |
| idMR:
|
MR3737120 |
| DOI:
|
10.14712/1213-7243.2015.221 |
| . |
| Date available:
|
2017-12-12T06:50:30Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146992 |
| . |
| Reference:
|
[1] Baird P.: Harmonic maps with symmetry, harmonic morphisms and deformation of metrics.Pitman Books Limited, Boston, MA, 1983, pp. 27–39. MR 0716320 |
| Reference:
|
[2] Baird P., Eells J.: A conservation law for harmonic maps.Lecture Notes in Math., 894, Springer, Berlin-New York, 1981, pp. 1–25. Zbl 0485.58008, MR 0655417, 10.1007/BFb0096222 |
| Reference:
|
[3] Baird P., Wood J.C.: Harmonic Morphisms between Riemannian Manifolds.London Mathematical Society Monographs, 29, Oxford University Press, Oxford, 2003. Zbl 1055.53049, MR 2044031 |
| Reference:
|
[4] Baird P., Kamissoko D.: On constructing biharmonic maps and metrics.Ann. Global Anal. Geom. 23 (2003), 65–75. Zbl 1027.31004, MR 1952859, 10.1023/A:1021213930520 |
| Reference:
|
[5] Baird P., Fardoun A., Ouakkas S.: Conformal and semi-conformal biharmonic maps.Ann. Global Anal. Geom. 34 (2008), 403–414. Zbl 1158.53049, MR 2447908, 10.1007/s10455-008-9118-8 |
| Reference:
|
[6] Balmus A.: Biharmonic properties and conformal changes.An. Stiint. Univ. Al. I. Cuza Iasi Mat. (N.S.) 50 (2004), 361–372. Zbl 1070.58016, MR 2131943 |
| Reference:
|
[7] Balmus A., Montaldo S., Oniciuc C.: Biharmonic maps between warped product manifolds.J. Geom. Phys. 57 (2008), 449–466. Zbl 1108.58011, MR 2271198, 10.1016/j.geomphys.2006.03.012 |
| Reference:
|
[8] Bertola M., Gouthier D.: Lie triple systems and warped products.Rend. Mat. Appl. (7) 21 (2001), 275–293. Zbl 1057.53020, MR 1884948 |
| Reference:
|
[9] Eells J., Lemaire L.: A report on harmonic maps.Bull. London Math. Soc. 16 (1978), 1–68. Zbl 0401.58003, MR 0495450, 10.1112/blms/10.1.1 |
| Reference:
|
[10] Eells J., Lemaire L.: Another report on harmonic maps.Bull. London Math. Soc. 20 (1988), 385–524. Zbl 0669.58009, MR 0956352, 10.1112/blms/20.5.385 |
| Reference:
|
[11] Eells J., Lemaire L.: Selected Topics in Harmonic Maps.CNMS Regional Conference Series of the National Sciences Foundation, November 1981. Zbl 0515.58011, MR 0703510 |
| Reference:
|
[12] Eells J., Ratto A.: Harmonic Maps and Minimal Immersions with Symmetries.Princeton University Press, Princeton, NJ, 1993. Zbl 0783.58003, MR 1242555 |
| Reference:
|
[13] Jiang G.Y.: $2$-harmonic maps and their first and second variational formulas.Chinese Ann. Math. Ser. A 7 (1986), 389–402. Zbl 1200.58015, MR 0886529 |
| Reference:
|
[14] Djaa N.E.H., Boulal A., Zagane A.: Generalized warped product manifolds and biharmonic maps.Acta Math. Univ. Comenian. 81 (2012), no. 2, 283–298. Zbl 1274.53093, MR 2975295 |
| Reference:
|
[15] Lu W.J.: Geometry of warped product manifolds and its five applications.PhD Thesis, Zhejiang University, 2013. |
| Reference:
|
[16] Lu W.J.: $f$-Harmonic maps of doubly warped product manifolds.Appl. Math. J. Chinese Univ. Ser. B 28 (2013), no. 2, 240–252. MR 3066461, 10.1007/s11766-013-2969-1 |
| Reference:
|
[17] Oniciuc C.: New examples of biharmonic maps in spheres.Colloq. Math. 97 (2003), 131–139. Zbl 1058.58003, MR 2010548, 10.4064/cm97-1-12 |
| Reference:
|
[18] Ouakkas S.: Biharmonic maps, conformal deformations and the Hopf maps.Diff. Geom. Appl. 26 (2008), 495–502. Zbl 1159.58009, MR 2458275, 10.1016/j.difgeo.2008.04.006 |
| Reference:
|
[19] Ou Y.-L.: p-harmonic morphisms, biharmonic morphisms, and non-harmonic biharmonic maps.J. Geom. Phys. 56 (2006), no. 3, 358–374. MR 2171890, 10.1016/j.geomphys.2005.02.005 |
| Reference:
|
[20] Perktas S.Y., Kilic E.: Biharmonic maps between doubly warped product manifolds.Balkan J. Geom. Appl. 15 (2010), no. 2, 159–170. Zbl 1225.58008, MR 2608547 |
| . |
