NOTES ON CRITICAL ALMOST HERMITIAN STRUCTURES

Title & Authors
NOTES ON CRITICAL ALMOST HERMITIAN STRUCTURES
Lee, Jung-Chan; Park, Jeong-Hyeong; Sekigawa, Kouei;

Abstract
We discuss the critical points of the functional $\small{F_{\lambda,\mu}(J,g)=\int_M(\lambda\tau+\mu\tau^*)d\upsilon_g}$ on the spaces of all almost Hermitian structures AH(M) with $\small{(\lambda,\mu){\in}R^2-(0,0)}$, where $\small{\tau}$ and $\small{\tau^*}$ being the scalar curvature and the *-scalar curvature of (J, g), respectively. We shall give several characterizations of Kahler structure for some special classes of almost Hermitian manifolds, in terms of the critical points of the functionals $\small{F_{\lambda,\mu}(J,g)}$ on AH(M). Further, we provide the almost Hermitian analogy of the Hilbert's result.
Keywords
critical almost Hermitian structure;Einstein-Hilbert functional;
Language
English
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