Harmonic Maps and the Topology of Conformally Compact Einstein Manifolds

Warped product and quasi-Einstein metrics

Warped products provide a rich class of physically significant geometric objects. Warped product construction is an important method to produce a new metric with a base manifold and a fibre. We construct compact base manifolds with a positive scalar curvature which do not admit any non-trivial quasi-Einstein warped product, and non compact complete base manifolds which do not admit any non-triv...

On the Topology of Conformally Compact Einstein 4-manifolds

In this paper we study the topology of conformally compact Einstein 4-manifolds. When the conformal infinity has positive Yamabe invariant and the renormalized volume is also positive we show that the conformally compact Einstein 4-manifold will have at most finite fundamental group. Under the further assumption that the renormalized volume is relatively large, we conclude that the conformally ...

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Algebraic Surfaces and 4-manifolds: Some Conjectures and Speculations

Introduction. Since the time of Riemann, there has been a close interplay between the study of the geometry of complex algebraic curves (or, equivalently, compact Riemann surfaces) and the topology of 2-manifolds. These connections arise from the uniformization theorem, which asserts that every simply connected Riemann surface is conformally equivalent to either the Riemann sphere, the plane, o...

Harmonic maps relative to α-connections on statistical manifolds

In this paper we study harmonic maps relative to α-connections, and not always relative to Levi-Civita connections, on statistical manifolds. In particular, harmonic maps on α-conformally equivalent statistical manifolds are discussed, and conditions for harmonicity are given by parameters α and dimensions n. As the application we also describe harmonic maps between level surfaces of a Hessian ...