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2004, Journal of the Australian Mathematical Society
We study the harmonicity of maps to or from cosymplectic manifolds by relating them to maps to or from Kähler spaces.
Rocky Mountain Journal of Mathematics, 2010
We prove that an (ϕ, J)-holomorphic maps from a compact cosymplectic manifold to a Kähler manifold is not only a harmonic map but also an energy minimizer on its homotopy class. We also prove a converse result.
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 2015
In the present paper we study the class of harmonic maps on cosymplectic manifolds. First we find the necessary and sufficient condition for the Riemannian map to be harmonic map between two cosymplectic manifolds and then from cosymplectic manifold to Sasakian manifold. Finally, we find the condition for non-existence of harmonic map from cosymplectic manifold to Kenmotsu manifold. Keywords Cosymplectic manifold Á Sasakian manifold Á Kenmotsu manifold Á Holomorphic map Á Harmonic map Á Riemannian map / 2 X ¼ ÀX þ gðXÞn; gðnÞ ¼ 1; gð/XÞ ¼ 0; /n ¼ 0; ð2:1Þ gð/X; /YÞ ¼ gðX; YÞ À gðXÞgðYÞ; ð2:2Þ gðn; nÞ ¼ 1; / n ¼ 0; g / ¼ 0; ð2:3Þ for any X, Y in TM. From Eq. (2.1) and (2.2), it can be seen that
In this note, we extend the definition of harmonic and biharmonic maps between two Riemannian manifolds, and we present some properties for f -harmonic maps and f -biharmonic maps.
2019
In this paper, we study harmonic map, pluriharmonicity and harmonic morphisms on trans-S-manifolds. Different results are discussed for different cases of trans-S-manifolds as trans-S-manifolds are the genralization of C-manifolds, f -Kenmotsu and S-manifolds. M.S.C. 2010: 53C55, 53C43, 58E20.
Journal of Geometry and Physics, 2011
We use functions of a bicomplex variable to unify the existing constructions of harmonic morphisms from a 3-dimensional Euclidean or pseudo-Euclidean space to a Riemannian or Lorentzian surface. This is done by using the notion of complex-harmonic morphism between complex-Riemannian manifolds and showing how these are given by bicomplex-holomorphic functions when the codomain is one-bicomplex dimensional. By taking real slices, we recover well-known compactifications for the three possible real cases. On the way, we discuss some interesting conformal compactifications of complex-Riemannian manifolds by interpreting them as bicomplex manifolds.
Journal of Geometry and Analysis, 2021
We introduce the natural notion of (p, q)-harmonic mor-phisms between Riemannian manifolds. This unifies several theories that have been studied during the last decades. We then study the special case when the maps involved are complex-valued. For these we find a characterisation and provide new non-trivial examples in important cases.
2009
The subject of harmonic maps is vast and has found many applications, and it would require a very long book to cover all aspects, even superficially. Hence, we have made a choice; in particular, highlighting the key questions
We construct the first known complex-valued harmonic morphisms from the non-compact Lie groups SL n (R), SU * (2n) and Sp(n, R) equipped with their standard Riemannian metrics.
We study in this paper harmonic maps and harmonic morphisms on S-manifolds. We also give some results and applications on the spectral theory of a harmonic map for which the target manifold is a S-space form. MSC: 53C55, 53C43, 58E20.
Glasgow Mathematical Journal, 2008
We consider transversally harmonic foliated maps between two Riemannian manifolds equipped with Riemannian foliations. We give various characterisations of such maps and we study the relation between the properties ‘harmonic’ and ‘transversally harmonic’ for a given map. We also consider these problems for particular classes of manifolds: manifolds with transversally almost Hermitian foliations and Riemannian flows.
We study in this paper harmonic maps and harmonic morphisms on Kenmotsu manifolds. We also give some results on the spectral theory of a harmonic map for which the target manifold is a Kenmotsu manifold.
arXiv: Differential Geometry, 2020
In this paper, we study the existence of harmonic and bi-harmonic maps into Riemannian manifolds admitting a conformal vector field, or a nontrivial Ricci solitons.
International Electronic Journal of Geometry
In this paper, we extend the definition of p-harmonic and p-biharmonic maps between Riemannian manifolds. We present some new properties for the generalized stable p-harmonic maps.
Arab Journal of Mathematical Sciences, 2017
In this note we characterize the harmonic maps and biharmonic maps with potential, and we prove that every biharmonic map with potential on a complete manifold satisfying some conditions is a harmonic map with potential.
2011
The aim of this paper is fourfold. Firstly, we introduce and study the f-ultra-harmonic maps. Secondly, we recall the geometric dynamics generated by a first order normal PDE system and we give original results regarding the geometric dynamics generated by other first order PDE systems. Thirdly, we determine the Gauss PDEs and the fundamental forms associated to integral manifolds of
Geom. Dedicata, 2015
We study 4-dimensional orientable Riemannian manifolds equipped with a minimal and conformal foliation F of codimension 2. We prove that the two adapted almost Hermitian structures J 1 and J 2 are both cosymplectic if and only if F is Riemannian and its horizontal distribution H is integrable.
Journal of Geometric Analysis, 1991
It has been conjectured that a lattice in a noncompact group of real rank one, other than SU(1, n), cannot be isomorphic to the fundamental group of a compact Kahler manifold; moreover, it is known to be true for SO(l, n). In this note it is shown that this conjecture also holds for the case of uniform lattices in F4(_20), the group of isometries of the Cayley hyperbolic plane. The result is a consequence of a classification theorem for harmonic maps between Kiihler and Cayley hyperbolic manifolds.
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