Critical Hermitian Structures on the Product of Sasakian Manifolds

Abstract

Let [Formula: see text] be a compact orientable smooth manifold admitting an almost complex structure and [Formula: see text] for (λ, μ) ∈ ℝ2 - (0, 0) be the functional defined on the space of the almost Hermitian structure [Formula: see text]. We discuss the first variational problem of the functional [Formula: see text] on the space [Formula: see text] and its subspace [Formula: see text] in the case where [Formula: see text] is a product manifold of Sasakian manifolds. Further this paper provides examples of critical Hermitian structures of the functional [Formula: see text] for various (λ, μ).