Harmonic Maps and Stability on f-Kenmotsu Manifolds
نویسنده
چکیده
In Section 2, we give preliminaries on f-Kenmotsu manifolds. The concept of f-Kenmotsu manifold, where f is a real constant, appears for the first time in the paper of Jannsens and Vanhecke 1 . More recently, Olszak and Roşca 2 defined and studied the f-Kenmotsu manifold by the formula 2.3 , where f is a function on M such that df ∧ η 0. Here, η is the dual 1-form corresponding to the characteristic vector field ξ of an almost contact metric structure on M. The condition df ∧ η 0 follows in fact from 2.3 if dimM ≥ 5. This does not hold in general if dimM 3. A 1-Kenmotsu manifold is a Kenmotsu manifold see Kenmotsu 3, 4 . Theorem 2.1 provides a geometric interpretation of an f-Kenmotsu structure. In Section 3, we initiate a study of harmonic maps when the domain is a compact fKenmotsu manifold and the target is a Kähler manifold. Ianus and Pastore 5, 6 defined a φ, J -holomorphic map between an almost contact metric manifold M φ, η, ξ, g and an almost Hermitian manifold N J, h as a smooth map F : M→N such that the condition F ◦ φ J ◦ F is satisfied. Then, the formula J τ F F divφ −Trgβ holds, where τ F is the tension field of F and β X,Y ̃ ∇XJ F Y ,
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ورودعنوان ژورنال:
- Int. J. Math. Mathematical Sciences
دوره 2008 شماره
صفحات -
تاریخ انتشار 2008