The parabolic Monge–Ampère equation on compact almost Hermitian manifolds

almost-quaternionic Hermitian manifolds

In this note we prove that if the fundamental 4-form of an almost-quaternionic Hermitian manifold (M,Q, g) of dimension 4n ≥ 8 satisfies the conformal-Killing equation, then (M,Q, g) is quaternionic-Kähler.

Analytic fields on compact balanced Hermitian manifolds

On a Hermitian manifold we construct a symmetric (1, 1)tensor H using the torsion and the curvature of the Chern connection. On a compact balanced Hermitian manifold we find necessary and sufficient conditions in terms of the tensor H for a harmonic 1-form to be analytic and for an analytic 1form to be harmonic. We prove that if H is positive definite then the first Betti number b1 = 0 and the ...

Curvature of Almost Quaternion- Hermitian Manifolds

We study the decomposition of the Riemannian curvature R tensor of an almost quaternion-Hermitian manifold under the action of its structure group Sp(n)Sp(1). Using the minimal connection, we show that most components are determined by the intrinsic torsion ξ and its covariant derivative ∇̃ξ and determine relations between the decompositions of ξ ⊗ ξ, ∇̃ξ and R. We pay particular attention to the...

Schrödinger Flow into Almost Hermitian Manifolds

ABSTRACT. We present a short-time existence theorem of solutions to the initial value problem for Schrödinger maps of a closed Riemannian manifold to a compact almost Hermitian manifold. The classical energy method cannot work for this problem since the almost complex structure of the target manifold is not supposed to be parallel with respect to the Levi-Civita connection. In other words, a lo...

On Multiplier Hermitian Structures on Compact Kähler Manifolds