NOTES ON CRITICAL ALMOST HERMITIAN STRUCTURES
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We discuss the critical points of the functional Ｆλ, μ (J, g) = ∫M (λτ+μτ* )dvg on the spaces of all almost Hermitian structures АН(M) with (λ,μ) ∈ R2 - (0,0),where τ and τ* being the scalar curvature and the *-scalar curvature of (J, g), respectively. We shall give several characterizations of Kähler structure for some special classes of almost Hermitian manifolds, in terms of the critical points of the functionals Fλ,μ(J,g) on АН(M). Further, we provide the almost Hermitian analogy of the Hilbert's result.
Abstract
We discuss the critical points of the functional Ｆλ, μ (J, g) = ∫M (λτ+μτ* )dvg on the spaces of all almost Hermitian structures АН(M) with (λ,μ) ∈ R2 - (0,0),where τ and τ* being the scalar curvature and the *-scalar curvature of (J, g), respectively. We shall give several characterizations of Kähler structure for some special classes of almost Hermitian manifolds, in terms of the critical points of the functionals Fλ,μ(J,g) on АН(M). Further, we provide the almost Hermitian analogy of the Hilbert's result.
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