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Some critical almost Kähler structures

Takashi OguroKouei Sekigawa — 2008

Colloquium Mathematicae

We consider the set of all almost Kähler structures (g,J) on a 2n-dimensional compact orientable manifold M and study a critical point of the functional λ , μ ( J , g ) = M ( λ τ + μ τ * ) d M g with respect to the scalar curvature τ and the *-scalar curvature τ*. We show that an almost Kähler structure (J,g) is a critical point of - 1 , 1 if and only if (J,g) is a Kähler structure on M.

A curvature identity on a 6-dimensional Riemannian manifold and its applications

Yunhee EuhJeong Hyeong ParkKouei Sekigawa — 2017

Czechoslovak Mathematical Journal

We derive a curvature identity that holds on any 6-dimensional Riemannian manifold, from the Chern-Gauss-Bonnet theorem for a 6-dimensional closed Riemannian manifold. Moreover, some applications of the curvature identity are given. We also define a generalization of harmonic manifolds to study the Lichnerowicz conjecture for a harmonic manifold “a harmonic manifold is locally symmetric” and provide another proof of the Lichnerowicz conjecture refined by Ledger for the 4-dimensional case under a...

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