Harmonicity of unit vector fields with respect to Riemannian g-natural metrics

被引:24
|
作者
Abbassi, M. T. K. [2 ]
Calvaruso, G. [1 ]
Perrone, D. [1 ]
机构
[1] Univ Lecce, Dipartimento Matemat E De Giorgi, I-73100 Lecce, Italy
[2] Univ Sidi Mohamed Ben Abdallah, Dept Math, Fac Sci Dhart El Mahraz, Fes, Fes, Morocco
关键词
Harmonic vector fields; Unit tangent sphere bundle; g-natural metrics; Reeb vector field; MANIFOLDS; 3-MANIFOLDS; MAPPINGS; BUNDLES; ENERGY;
D O I
10.1016/j.difgeo.2008.06.016
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let (M, g) be a compact Riemannian manifold and T1M its unit tangent sphere bundle. Unit vector fields defining harmonic maps from (M, g) to (T1M, (g) over bar (s)), (g) over bar (s) being the Sasaki metric on T1M, have been extensively studied. The Sasaki metric, and other well known Riemannian metrics on T1M, are particular examples of g-natural metrics. We equip T1M with an arbitrary Riemannian g-natural metric (G) over bar, anti investigate the harmonicity of a unit vector field V of M, thought as a map from (M, g) to (T1M, (G) over bar). We then apply this study to characterize unit Killing vector fields and to investigate harmonicity properties of the Reeb vector field of a contact metric manifold. (C) 2008 Elsevier B.V. All rights reserved.
引用
收藏
页码:157 / 169
页数:13
相关论文
共 49 条
  • [21] g-NATURAL METRICS ON TANGENT BUNDLES AND JACOBI OPERATORS
    Degla, S.
    Todjihounde, L.
    ACTA MATHEMATICA UNIVERSITATIS COMENIANAE, 2011, 80 (02): : 255 - 269
  • [22] On Riemannian g-natural Metrics of the Form a.gs + b.gh + c.gv on the Tangent Bundle of a Riemannian Manifold (M, g)
    Mohamed Tahar Kadaoui Abbassi
    Maâti Sarih
    Mediterranean Journal of Mathematics, 2005, 2 : 19 - 43
  • [23] INVARIANCE OF g-NATURAL METRICS ON LINEAR FRAME BUNDLES
    Kowalski, Oldrich
    Sekizawa, Masami
    ARCHIVUM MATHEMATICUM, 2008, 44 (02): : 139 - 147
  • [24] g-NATURAL METRICS OF CONSTANT SECTIONAL CURVATURE ON TANGENT BUNDLES
    Degla, S.
    Ezin, J. -P.
    Todjihounde, L.
    INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY, 2009, 2 (01): : 74 - 94
  • [25] Weakly symmetry of a class of g-natural metrics on tangent bundles
    E. Peyghan
    Journal of Contemporary Mathematical Analysis, 2016, 51 : 167 - 172
  • [26] Magnetic trajectories on tangent sphere bundle with g-natural metrics
    Abbassi, Mohamed Tahar Kadaoui
    Amri, Noura
    Munteanu, Marian Ioan
    ANNALI DI MATEMATICA PURA ED APPLICATA, 2021, 200 (03) : 1033 - 1054
  • [27] Magnetic trajectories on tangent sphere bundle with g-natural metrics
    Mohamed Tahar Kadaoui Abbassi
    Noura Amri
    Marian Ioan Munteanu
    Annali di Matematica Pura ed Applicata (1923 -), 2021, 200 : 1033 - 1054
  • [28] Weakly Symmetry of a Class of g-Natural Metrics on Tangent Bundles
    Peyghan, E.
    JOURNAL OF CONTEMPORARY MATHEMATICAL ANALYSIS-ARMENIAN ACADEMY OF SCIENCES, 2016, 51 (04): : 167 - 172
  • [29] Geodesible vector fields and adapted invariant Riemannian metrics
    Pripoae, Gabriel-Teodor
    Pripoae, Cristina-Liliana
    BSG PROCEEDINGS 16, 2009, 16 : 139 - +
  • [30] Bochner flatness of tangent bundles with g-natural almost Hermitian metrics
    David E. Blair
    Handan Yıldırım
    Annals of Global Analysis and Geometry, 2016, 49 : 259 - 269