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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2023.5
- 수록면
- 109 - 129 (21page)
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In this paper, we introduce a second order linear differential operator $ \stackrel{T}{\Box}:C^\infty(M)\rightarrow C^\infty(M) $ as a natural generalization of Cheng-Yau operator, \cite{Yauoperator}, where $ T $ is a $ (1,1) $-tensor on Riemannian manifold $ (M,h) $, and then we show on compact Riemannian manifolds, divT=divT^t, and if divT = 0, and f be a smooth function on M, the condition $ \stackrel{T}{\Box}f=0 implies that f is constant. Hereafter, we introduce T-energy functionals and by deriving variations of these functionals, we define T-harmonic maps between Riemannian manifolds, which is a generalization of L_{k}-harmonic maps introduced in [3]. Also we have studied f$ T $-harmonic maps for conformal immersions and as application of it, we consider f$ L $ _{k}-harmonic hyper- surfaces in space forms, and after that we classify complete f$L$_{1}-harmonic surfaces, some f$L$_{k}-harmonic isoparametric hypersurfaces, f$L$_{k}-harmonic weakly convex hypersurfaces, and we show that there exists no compact f$L$_{k}-harmonic hypersurface either in the Euclidean space or in the hyperbolic space or in the Euclidean hemisphere. As well, some properties and examples of these definitions are given.
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