• 제목/요약/키워드: conformal maps

검색결과 18건 처리시간 0.019초

HARMONIC AND BIHARMONIC MAPS ON DOUBLY TWISTED PRODUCT MANIFOLDS

  • Boulal, Abdelhamid;Djaa, Mustapha;Ouakkas, Seddik
    • 대한수학회논문집
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    • 제33권1호
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    • pp.273-291
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    • 2018
  • In this paper we investigate the geometry of doubly twisted product manifolds and we study the harmonicity and biharmonicity of maps between doubly twisted product Riemannian manifold. Also we characterize the conformal biharmonic maps and construct some new proper biharmonic maps.

ON THE CONFORMAL TRIHARMONIC MAPS

  • Ouakkas, Seddik;Reguig, Yasmina
    • 대한수학회논문집
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    • 제37권2호
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    • pp.607-629
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    • 2022
  • In this paper, we give the necessary and sufficient condition for the conformal mapping ϕ : (ℝn, g0) → (Nn, h) (n ≥ 3) to be triharmonic where we prove that the gradient of its dilation is a solution of a fourth-order elliptic partial differential equation. We construct some examples of triharmonic maps which are not biharmonic and we calculate the trace of the stress-energy tensor associated with the triharmonic maps.

SOME RESULTS ON THE GEOMETRY OF A NON-CONFORMAL DEFORMATION OF A METRIC

  • Djaa, Nour Elhouda;Zagane, Abderrahim
    • 대한수학회논문집
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    • 제37권3호
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    • pp.865-879
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    • 2022
  • Let (Mm, g) be an m-dimensional Riemannian manifold. In this paper, we introduce a new class of metric on (Mm, g), obtained by a non-conformal deformation of the metric g. First we investigate the Levi-Civita connection of this metric. Secondly we characterize the Riemannian curvature, the sectional curvature and the scalar curvature. In the last section we characterizes some class of proper biharmonic maps. Examples of proper biharmonic maps are constructed when (Mm, g) is an Euclidean space.

f-BIHARMONIC SUBMANIFOLDS AND f-BIHARMONIC INTEGRAL SUBMANIFOLDS IN LOCALLY CONFORMAL ALMOST COSYMPLECTIC SPACE FORMS

  • Aslam, Mohd;Karaca, Fatma;Siddiqui, Aliya Naaz
    • 대한수학회논문집
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    • 제37권2호
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    • pp.595-606
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    • 2022
  • In this paper, we have studied f-biharmonic submanifolds in locally conformal almost cosymplectic space forms and have derived condition on second fundamental form for f-biharmonic submanifolds. Also, we have discussed its integral submanifolds in locally conformal almost cosymplectic space forms.

A NOTE ON HARMONIC MAPPINGS

  • Hong, Suk Ho
    • Korean Journal of Mathematics
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    • 제4권1호
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    • pp.65-70
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    • 1996
  • In this note, we study a relation between harmonic maps and exponential harmonic maps, and we show existence of Yang-Mills connections.

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A MONOTONICITY FORMULA AND A LIOUVILLE TYPE THEOREM OF V-HARMONIC MAPS

  • Zhao, Guangwen
    • 대한수학회보
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    • 제56권5호
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    • pp.1327-1340
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    • 2019
  • We establish a monotonicity formula of V-harmonic maps by using the stress-energy tensor. Use the monotonicity formula, we can derive a Liouville type theorem for V-harmonic maps. As applications, we also obtain monotonicity and constancy of Weyl harmonic maps from conformal manifolds to Riemannian manifolds and ${\pm}holomorphic$ maps between almost Hermitian manifolds. Finally, a constant boundary-value problem of V-harmonic maps is considered.

A STUDY ON THE EFFECTIVE ALGORITHMS BASED ON THE WEGMANN'S METHOD

  • Song, Eun-Jee
    • Journal of applied mathematics & informatics
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    • 제20권1_2호
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    • pp.595-602
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    • 2006
  • Determinations of conformal map from the unit disk onto a Jordan region are reduced to solve the Theodorsen equation which is an integral equation for the boundary correspondence function. Among numerical conformal maps the Wegmann's method is well known as a Newton efficient one for solving Theodorsen equation. However this method has not so wide class of convergence. We proposed as an improved method for convergence by applying a low frequency filter to the Wegmann's method. In this paper, we investigate error analysis and propose an automatic algorithm based on this analysis.

ON A RIGIDITY OF HARMONIC DIFFEOMORPHISM BETWEEN TWO RIEMANN SURFACES

  • KIM, TAESOON
    • 호남수학학술지
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    • 제27권4호
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    • pp.655-663
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    • 2005
  • One of the basic questions concerning harmonic map is on the existence of harmonic maps satisfying a certain condition. Rigidity of a certain harmonic map can be considered as an answer for this kinds of questions. In this article, we study a rigidity property of harmonic diffeomorphisms under the condition that the inverse map is also harmonic. We show that every such a harmonic diffeomorphism is totally geodesic or conformal in two dimensional case.

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HARMONICITY OF ALMOST NORDEN SUBMERSIONS BETWEEN ALMOST NORDEN MANIFOLDS

  • Gupta, Garima;Kumar, Rakesh;Rani, Rachna;Sachdeva, Rashmi
    • 대한수학회보
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    • 제59권2호
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    • pp.375-395
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    • 2022
  • We define an almost Norden submersion (holomorphic and semi-Riemannian submersion) between almost Norden manifolds and show that, in most of the cases, the base manifold has the similar kind of structure as that of total manifold. We obtain necessary and sufficient conditions for almost Norden submersion to be a totally geodesic map. We also derive decomposition theorems for the total manifold of such submersions. Moreover, we study the harmonicity of almost Norden submersions between almost Norden manifolds and between Kaehler-Norden manifolds. Finally, we derive conditions for an almost Norden submersion to be a harmonic morphism.