On 1-harmonic functions.
On generalized -harmonic morphisms
In this paper, we study the characterization of generalized -harmonic morphisms between Riemannian manifolds. We prove that a map between Riemannian manifolds is an -harmonic morphism if and only if it is a horizontally weakly conformal map satisfying some further conditions. We present new properties generalizing Fuglede-Ishihara characterization for harmonic morphisms ([Fuglede B., Harmonic morphisms between Riemannian manifolds, Ann. Inst. Fourier (Grenoble) 28 (1978), 107–144], [Ishihara T., A...
On sectional Newtonian graphs
In this paper, we introduce the so-called sectional Newtonian graphs for univariate complex polynomials, and study some properties of those graphs. In particular, we list all possible sectional Newtonian graphs when the degrees of the polynomials are less than five, and also show that every stable gradient graph can be realized as a polynomial sectional Newtonian graph.
On the biharmonicity of product maps.
On the degeneration of harmonic sequences from surfaces into complex Grassmann manifolds
Let be a harmonic map from surface into complex Grassmann manifold. In this paper, some sufficient conditions for the harmonic sequence generated by to have degenerate -transform or -transform are given.
On the geometry of some solvable extensions of the Heisenberg group
In this paper we first classify left-invariant generalized Ricci solitons on some solvable extensions of the Heisenberg group in both Riemannian and Lorentzian cases. Then we obtain the exact form of all left-invariant unit time-like vector fields which are spatially harmonic. We also calculate the energy of an arbitrary left-invariant vector field on these spaces and obtain all vector fields which are critical points for the energy functional restricted to vector fields of the same length. Furthermore,...
On the Jäger-Kaul theorem concerning harmonic maps
On the twistor bundle of de Sitter space .
On weakly harmonic maps from Finsler to riemannian manifolds