On the bi-harmonic maps with potential
نویسندگان
چکیده
منابع مشابه
ON f -BI-HARMONIC MAPS BETWEEN RIEMANNIAN MANIFOLDS
A. Both bi-harmonic map and f -harmonic map have nice physical motivation and applications. In this paper, by combination of these two harmonic maps, we introduce and study f -bi-harmonic maps as the critical points of the f -bi-energy functional 1 2 ∫ M f |τ(φ)| dvg. This class of maps generalizes both concepts of harmonic maps and biharmonic maps. We first derive the f -biharmonic map ...
متن کاملBi-harmonic Functions on Groups
| Two natural deenitions of bi-harmonic functions on countable groups are shown to essentially coincide. Criteria of absence of non-constant bounded bi-harmonic functions are formulated. A description of these functions for free groups is given. Fonctions bi-harmoniques sur les groupes R esum e R esum e | Nous montrons l' equivalence essentielle de deux d eenitions naturelles des fonctions bi-h...
متن کاملLectures on Harmonic Maps
§1 Background and Setup Let M be an m-dimensional, compact, Riemannian manifold endowed with the metric dsM = gij dx i dx , where {x, x, · · · , x} is a local coordinate system of M. Suppose N is an n-dimensional, complete, Riemannian manifold with metric given by dsN = hαβ du α du , where {u, u, · · · , u} is a local coordinate system of N. Let f : M → N be a C mapping from M into N . Definiti...
متن کاملOn Homotopic Harmonic Maps
(1.1) M' is complete and its sectional curvatures are non-positive. In terms of local coordinates x = (x, . . . , x) on M and y = (y, . . . , y) on M', let the respective Riemann elements of arc-length be ds = gij dx dx\ ds' = g'a$ dy a dy& and r^-fc, T'Vy be the corresponding Christoffel symbols. When there is no danger of confusion, x (or y) will represent a point of M (or M') or its coordina...
متن کاملHarmonic maps on spaces with conical singularities
© Bulletin de la S. M. F., 1992, tous droits réservés. L’accès aux archives de la revue « Bulletin de la S. M. F. » (http://smf. emath.fr/Publications/Bulletin/Presentation.html) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impress...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Arab Journal of Mathematical Sciences
سال: 2018
ISSN: 1319-5166
DOI: 10.1016/j.ajmsc.2017.06.001