Related papers: Centrally Harmonic spaces

In this note, we show that for any harmonic map into a non-compact symmetric space one can find naturally a "dual" harmonic map into a compact symmetric space which can be constructed from the same basic data (called "potentials" in the…

Harmonicity of holomorphic maps between various subclasses of almost contact metric manifolds is discussed. Consequently, some new results are obtained. Also some known results are recovered, some of them are generalized and some of them…

Recently the authors have explored new concepts of plurisubharmonicity and pseudoconvexity, with much of the attendant analysis, in the context of calibrated manifolds. Here a much broader extension is made. This development covers a wide…

Complex manifolds with compatible metric have a naturally defined subspace of harmonic differential forms that satisfy Serre, Hodge, and conjugation duality, as well as hard Lefschetz duality. This last property follows from a…

In this talk, I will discuss the use of harmonic functions to study the geometry and topology of complete manifolds. In my previous joint work with Luen-fai Tam, we discovered that the number of infinities of a complete manifold can be…

We examine some kinds of discrete symmetries which are dynamically preserved, using the (generalized) Gowdy models of the first kind.

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…

Synchronization of coupled harmonic oscillators is investigated. Coupling considered here is pairwise, unidirectional, and described by a nonlinear function (whose graph resides in the first and third quadrants) of some projection of the…

We will discuss the following results C_n complexification of R(n) spaces, C_n structure and the invariant surfaces C_n holomorphicity and harmonicity. We also consider the link between C_n holomorphicity and the origin of spin 1/n. In our…

We first study $f$-biharmonicity of totally umbilical hypersurfaces in a generic Riemannian manifold and then prove that any totally umbilical proper $f$-biharmonic hypersurface in a nonpositively curved manifold has to be noncompact. We…

We characteristize those Einstein four manifolds which are locally symmetric spaces of noncompact type. Namely they are four manifolds which admit solutions to the (non-Abelian) Seiberg Witten equations and satisty certain characterisitc…

Representations of four-dimensional superconformal groups on harmonic superfields are discussed. It is argued that any representation can be given as a superfield on many superflag manifolds. Representations on analytic superspaces do not…

This paper is a sequel to [Caine A., Pickrell D., arXiv:0710.4484], where we studied the Hamiltonian systems which arise from the Evens-Lu construction of homogeneous Poisson structures on both compact and noncompact type symmetric spaces.…

We give a new categorical way to construct the central stability homology of Putman and Sam and explain how it can be used in the context of representation stability and homological stability. In contrast to them, we cover categories with…

We prove that closed manifolds admitting a generic metric whose sectional curvature is locally quasi-constant are graphs of space forms. In the more general setting of QC spaces where sets of isotropic points are arbitrary, under suitable…

Coarse geometry, the branch of topology that studies the global properties of spaces, was originally developed for metric spaces and then Roe introduced coarse structures as a large-scale counterpart of uniformities. In the literature,…

We make a further step in the unisolvence open problem for unsymmetric Kansa collocation, proving nonsingularity of Kansa matrices with polyharmonic splines and random fictitious centers, for second-order elliptic equations with mixed…

In this paper, we consider certain topological properties along with certain types of mappings on these spaces defined by the notion of ideal convergence. In order to do that, we primarily follow in the footsteps of the earlier studies of…

We study submanifolds whose principal curvatures, counted with multiplicities, do not depend on the normal direction. Such submanifolds, which we briefly call CPC submanifolds, are always austere, hence minimal, and have constant principal…

In the present paper, we derive several conditions of linear combinations and convolutions of harmonic mappings to be univalent and convex in one direction, one of them gives a partial answer to an open problem proposed by Dorff. The…