On structure-preserving connections
In this paper we find the formula of connections under which an almost complex structure is covariantly constant. These types of connections on anti-Kähler–Codazzi manifolds are described. Also, twin metric-preserving connections are analyzed for quasi-Kähler manifolds. Finally, anti-Hermitian Chern connections are investigated.
KeywordsAlmost complex structure Semi-Riemannian metric Anti-Hermitian structure Anti-Kähler–Codazzi manifold Anti-Kähler manifold Quasi-Kähler manifold Chern connection
Mathematics Subject Classification53C15 53C05