Related papers: Polyharmonic hypersurfaces into pseudo-Riemannian …

We study biharmonic maps between Riemannian manifolds with finite energy and finite bi-energy. We show that if the domain is complete and the target of non-positive curvature, then such a map is harmonic. We then give applications to…

Pluriharmonic maps form an important class of harmonic maps which includes holomorphic maps. We study their morphisms, in particular the inter-relationships between $(1,1)$-geodesic, pluriharmonic and $\pm$holomorphic maps. Then we…

We consider supersymmetric field theories on compact manifolds M and obtain constraints on the parameter dependence of their partition functions Z_M. Our primary focus is the dependence of Z_M on the geometry of M, as well as background…

We describe for any Riemannian manifold a certain infinitesimal neighbourhood of the diagonal. Semi-conformal maps are analyzed as those that preserve such neighbourhoods; harmonic maps are analyzed as those that preserve mirror image…

Let $M^n$ be a closed Riemannian manifold on which the integral of the scalar curvature is nonnegative. Suppose $\mathfrak{a}$ is a symmetric $(0,2)$ tensor field whose dual $(1,1)$ tensor $\mathcal{A}$ has $n$ distinct eigenvalues, and…

We consider a complete biharmonic hypersurface with nowhere zero mean curvature vector field $\phi:(M^m,g)\rightarrow (S^{m+1},h)$ in a sphere. If the squared norm of the second fundamental form $B$ is bounded from above by m, and $\int_M…

We characterize biharmonic anti-invariant surfaces in $3$-dimensional generalized $(\kappa, \mu)$-manifolds with non-zero constant mean curvature by means of the scalar curvature of the ambient space and the mean curvature. In addition, we…

We study hypersurfaces either in the De Sitter space $\S_1^{n+1}\subset\R_1^{n+2}$ or in the anti De Sitter space $\H_1^{n+1}\subset\R_2^{n+2}$ whose position vector $\psi$ satisfies the condition $L_k\psi=A\psi+b$, where $L_k$ is the…

The classification problem for holonomy of pseudo-Riemannian manifolds is actual and open. In the present paper, holonomy algebras of Lorentz-K\"ahler manifolds are classified. A simple construction of a metric for each holonomy algebra is…

Let $M$ be a closed orientable hypersurface of dimension $n$, with nonwhere vanishing mean curvature $H$, immersed into a Riemannian Spin$^c$ manifold $\mathcal Z$ carrying a parallel spinor field. The first eigenvalue…

We prove that for any two closed Riemannian manifolds $M^{2m}$ ($m\geq 1$) and $N$, there exists a minimizing (extrinsic) $m$-polyharmonic map for every free homotopy class in $[M^{2m}, N]$, provided that the homotopy group $\pi_{2m}(N)$ is…

In [14], it was shown that, if M is a 3-dimensional asymptotically harmonic with minimal horospheres, then M is flat. However, there is a gap in the proof of this paper. In this paper, we provide the correct proof of the result. Thus we…

This paper starts by introducing results from geometric measure theory to prove symmetric decreasing rearrangement inequalities on $\mathbb{R}^n$, which give multiple proofs of the isoperimetric and P\'{o}lya-Szeg\H{o} inequalities. Then we…

We give a complete classification of Riemannian and Lorentzian surfaces of arbitrary codimension in a pseudo-sphere whose pseudo-spherical Gauss maps are of 1-type or, in particular, harmonic. In some cases a concrete global classification…

We give necessary and sufficient conditions for Riemannian maps to be biharmonic. We also define pseudo umbilical Riemannian maps as a generalization of pseudo-umbilical submanifolds and show that such Riemannian maps put some restrictions…

The current paper discusses some new results about conformal polynomic surface parameterizations. A new theorem is proved: Given a conformal polynomic surface parameterization of any degree it must be harmonic on each component. As a first…

In this paper we consider the Balmu\c{s}-Montaldo-Oniciuc's conjecture in the case of hemispheres. We prove that a compact non-minimal biharmonic hypersurface in a hemisphere of $S^{n+1}$ must be the small hypersphere…

In this paper we consider a complete connected noncompact Riemannian manifold M with Ricci curvature bounded from below, positive injectivity radius and spectral gap b. We introduce a sequence X^1(M), X^2(M), ... of new Hardy spaces on M,…

Following our approach to metric Lie algebras developed in math.DG/0312243 we propose a way of understanding pseudo-Riemannian symmetric spaces which are not semi-simple. We introduce cohomology sets (called quadratic cohomology) associated…

We prove the equivalence of several natural notions of conformal maps between sub-Riemannian manifolds. Our main contribution is in the setting of those manifolds that support a suitable regularity theory for subelliptic $p$-Laplacian…