Generic submanifolds of a locally conformal Kaehler manifold. II.
On Some 4-Dimensional Compact Einstein Almost Kähler Manifolds.
Hermitian surfaces of constant holomorphic sectional curvature.
Non-existence of almost Kähler structure on hyperbolic spaces of dimension 2n(...4).
Some critical almost Kähler structures
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 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 if and only if (J,g) is a Kähler structure on M.
Harmonic maps and -regular manifolds
Four-dimensional curvature homogeneous spaces
We prove that a four-dimensional, connected, simply connected and complete Riemannian manifold which is curvature homogeneous up to order two is a homogeneous Riemannian space.
A curvature identity on a 6-dimensional Riemannian manifold and its applications
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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