Abstract The natural symmetries of Riemannian manifolds are described by the its Riemann curvature tensor. In that sense, most symmetric constant sectional ones. Its generalizations locally manifolds, semisymmetric and pseudosymmetric manifolds. analogous holomorphic Kaehler holomorphically Do they differ in some way from their analogues? Yes, we prove can all be characterized only terms planes...

Let (M, g, J) be a compact Hermitian manifold with a smooth boundary. Let ∆p,B and ⊓ ⊔p,B be the realizations of the real and complex Laplacians on p forms with either Dirichlet or Neumann boundary conditions. We generalize previous results in the closed setting to show that (M, g, J) is Kaehler if and only if Spec(∆p,B) = Spec(2 ⊓ ⊔p,B) for p = 0, 1. We also give a characterization of manifold...

Generalizing the construction of the Maslov class [µ Λ ] for a La-grangian embedding in a symplectic vector space, we prove that it is possible to give a consistent definition of the class [µ Λ ] for any La-grangian submanifold of a Calabi-Yau manifold. Moreover, extending a result of Morvan in symplectic vector spaces, we prove that [µ Λ ] can be represented by i H ω, where H is the mean curva...

A theorem of Cantat and Urech says that an analog the classical Tits alternative holds for group birational automorphisms a compact complex Kaehler surface. We established in our previous paper following Tits-type alternative: if X is toric affine variety G subgroup Aut(X) generated by finite set unipotent subgroups normalized acting torus then either contains nonabelian free or algebraic group...