Harmonic maps relative to α-connections on statistical manifolds

Harmonic maps relative to α-connections of statistical manifolds

In this paper, we study harmonic maps relative to α-connections, but not necessarily standard harmonic maps. A standard harmonic map is defined by the first variation of the energy functional of a map. A harmonic map relative to an α-connection is defined by an equation similar to a first variational equation, though it is not induced by the first variation of the standard energy functional. In...

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Harmonic Morphisms between Riemannian Manifolds

Harmonic morphisms are mappings between Riemannian manifolds which preserve Laplace’s equation. They can be characterized as harmonic maps which enjoy an extra property called horizontal weak conformality or semiconformality. We shall give a brief survey of the theory concentrating on (i) twistor methods, (ii) harmonic morphisms with one-dimensional fibres; in particular we shall outline the co...

Principal Bundles over Statistical Manifolds

In this paper, we introduce the concept of principal bundles on statistical manifolds. After necessary preliminaries on information geometry and principal bundles on manifolds, we study the α-structure of frame bundles over statistical manifolds with respect to α-connections, by giving geometric structures. The manifold of one-dimensional normal distributions appears in the end as an applicatio...

Harmonic maps on domains with piecewise Lipschitz continuous metrics

For a bounded domain Ω equipped with a piecewise Lipschitz continuous Riemannian metric g, we consider harmonic map from (Ω, g) to a compact Riemannian manifold (N, h) ↪→ Rk without boundary. We generalize the notion of stationary harmonic maps and prove their partial regularity. We also discuss the global Lipschitz and piecewise C1,α-regularity of harmonic maps from (Ω, g) to manifolds that su...