By making use of the symplectic reduction and the cohomogeneity method, we give a general method for constructing Hamiltonian minimal submanifolds in Kaehler manifolds with symmetries. As applications, we construct infinitely many nontrivial complete Hamiltonian minimal submanifolds in CP n and Cn.

In a previous paper we built a modified Hamiltonian formalism to make possible explicit maps among manifolds. In this paper the modified formalism was generalized. As an application, we have built maps among spaces associated to spinors, as well as maps among Kaehler spaces. ∗ E-mail: [email protected]

In this work, we first establish short time existence and Shi's type estimate of second Ricci flow on complete noncompact Hermitian manifolds. As an application, use the to discuss Kaehler-Einstein metric

In this note we adapt the work of Hall to find quasi-Einstein metrics on sphere bundles over products Fano Kaehler-Einstein manifolds, as well where only one end is blown down.