Harmonic Maps on Kenmotsu Manifolds (original) (raw)
Harmonic maps on generalized metric manifolds
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.
Harmonic maps and cosymplectic manifolds
Journal of the Australian Mathematical Society, 2004
We study the harmonicity of maps to or from cosymplectic manifolds by relating them to maps to or from Kähler spaces.
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.
Biharmonic maps on kenmotsu manifolds
New Trends in Mathematical Science, 2016
In this paper we study biharmonic maps on Kenmotsu manifolds. An example for biharmonic map of a three-Kenmotsu manifold is constructed for illustration.
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
Harmonic Morphisms Projecting Harmonic Functions to Harmonic Functions
For Riemannian manifolds M and N, admitting a submersion φ with compact fibres, we introduce the projection of a function via its decomposition into horizontal and vertical components. By comparing the Laplacians on M and N, we determine conditions under which a harmonic function on U φ −1 V ⊂ M projects down, via its horizontal component, to a harmonic function on V ⊂ N.
Harmonic maps, morphisms and globally null manifolds
International Journal of Pure and Applied Mathematics
This paper deals with a new class of harmonic maps and morphisms into globally null manifolds which admit a global null vector field and a complete Riemannian hypersurface. We concentrate on the fundamental existence problem of harmonic maps and morphisms for this new class and establish an interplay between harmonic maps, morphisms, globally null manifolds and globally hyperbolic spacetimes of general relativity.
Harmonic morphisms between riemannian manifolds
Annales de l’institut Fourier, 1978
A smooth map f : M → N between semi-riemannian manifolds is called a harmonic morphism if f pulls back harmonic functions (i.e., local solutions of the Laplace-Beltrami equation) on N into harmonic functions on M. It is shown that a harmonic morphism is the same as a harmonic map which is moreover horizontally weakly conformal, these two notions being likewise carried over from the riemannian case. Additional characterizations of harmonic morphisms are given. The case where M and N have the same dimension n is studied in detail. When n = 2 and the metrics on M and N are indefinite, the harmonic morphisms are characterized essentially by preserving characteristics.