On Nearly-Kähler Geometry

By P. Nagy. 2002

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Homogeneous nearly K\"{a}hler manifolds (2006, background): “Finally, irreducible nearly Khler manifolds are (i) 3-symmetric of type B or (ii) 6-dimensional. c. Eventually, Nagy has proved in [36], corollary 3.1, that the complete, simply connected, real reducible, nearly Khler manifolds are 3-symmetric of type C.”
Maximally homogeneous para-CR manifolds of semisimple type (2006, unknown): “ctually symmetric and Jinvariant. The Hermitian Ricci tensor is related to the usual Riemannian one by (4.2) Ric= Ric− 3 4 r as implied by the general curvature comparison formula (3.2). Theorem 4.2. [48] Let (M2m,g,J) be a strict nearly-Kahler manifold. The following hold: (i) the Ricci tensor of t”
Six-Dimensional Nearly Kähler Manifolds of Cohomogeneity One (II) (2009, background): “Recently Nagy proved the following two structure results: a) any NK manifold is locally holomorphically isometric to the product of a Kähler manifold and a strict NK manifold; b) any complete strict NK manifold is finitely covered by a product of homogeneous 3-symmetric manifolds, twistor spaces of ”
Classification des variété approximativement kähleriennes homogénes (2004, background): “Geom 22, 167–178 (2002) [14] P.A. Nagy, Nearly Kähler geometry and Riemannian foliations, Asian J. Math.”