| Title:
|
On generalized $f$-harmonic morphisms (English) |
| Author:
|
Cherif, A. Mohammed |
| Author:
|
Mustapha, Djaa |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
55 |
| Issue:
|
1 |
| Year:
|
2014 |
| Pages:
|
17-27 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we study the
characterization of generalized
$f$-harmonic morphisms between Riemannian
manifolds. We prove that a map between
Riemannian manifolds is an
$f$-harmonic morphism if and only if it
is a horizontally weakly conformal map
satisfying some further conditions.
We present new properties generalizing
Fuglede-Ishihara characterization for
harmonic morphisms ([Fuglede B.,
Harmonic morphisms between Riemannian
manifolds, Ann. Inst. Fourier (Grenoble)
28 (1978), 107--144], [Ishihara T.,
A mapping of Riemannian manifolds which
preserves harmonic functions,
J. Math. Kyoto Univ. 19 (1979),
no. 2, 215--229]). (English) |
| Keyword:
|
$f$-harmonic morphisms |
| Keyword:
|
$f$-harmonic maps |
| Keyword:
|
horizontally weakly conformal map |
| MSC:
|
53C43 |
| MSC:
|
58E20 |
| idZBL:
|
Zbl 06383782 |
| idMR:
|
MR3160823 |
| . |
| Date available:
|
2014-01-17T09:32:05Z |
| Last updated:
|
2016-04-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143565 |
| . |
| Reference:
|
[1] Ara M.: Geometry of $F$-harmonic maps.Kodai Math. J. 22 (1999), no. 2, 243–263. Zbl 0941.58010, MR 1700595, 10.2996/kmj/1138044045 |
| Reference:
|
[2] Baird P., Wood J.C.: Harmonic Morphisms between Riemannain Manifolds.Clarendon Press, Oxford, 2003. MR 2044031 |
| Reference:
|
[3] Course N.: f-harmonic maps which map the boundary of the domain to one point in the target.New York J. Math. 13 (2007), 423–435 (electronic). Zbl 1202.58012, MR 2357720 |
| Reference:
|
[4] Djaa M., Cherif A.M., Zegga K., Ouakkas S.: On the generalized of harmonic and bi-harmonic maps.Int. Electron. J. Geom. 5 (2012), no. 1, 90–100. MR 2915490 |
| Reference:
|
[5] Mustapha D., Cherif A.M.: On the generalized $f$-biharmonic maps and stress $f$-bienergy tensor.Journal of Geometry and Symmetry in Physics, JGSP 29 (2013), 65–81. MR 3113559 |
| Reference:
|
[6] Fuglede B.: Harmonic morphisms between Riemannian manifolds.Ann. Inst. Fourier (Grenoble) 28 (1978), 107–144. Zbl 0408.31011, MR 0499588, 10.5802/aif.691 |
| Reference:
|
[7] Gudmundsson S.: The geometry of harmonic morphisms.University of Leeds, Department of Pure Mathematics, April 1992. Zbl 0715.53029 |
| Reference:
|
[8] Ishihara T.: A mapping of Riemannian manifolds which preserves harmonic functions.J. Math. Kyoto Univ. 19 (1979), no. 2, 215–229. Zbl 0421.31006, MR 0545705 |
| Reference:
|
[9] Lichnerowicz A.: Applications harmoniques et variétés Kähleriennes.1968/1969 Symposia Mathematica, Vol. III (INDAM, Rome, 1968/69), pp. 341–402, Academic Press, London. Zbl 0193.50101, MR 0262993 |
| Reference:
|
[10] Ou Y.L.: On $f$-harmonic morphisms between Riemannian manifolds.arxiv:1103.5687, Chinese Ann. Math., series B(to appear). |
| Reference:
|
[11] Ouakkas S., Nasri R., Djaa M.: On the f-harmonic and f-biharmonic maps.JP J. Geom. Topol. 10 (2010), no. 1, 11–27. Zbl 1209.58014, MR 2677559 |
| . |
