Let  be an n-dimensional Riemannian manifold, and  be its tangent bundle with the lift metric. Then every infinitesimal fiber-preserving conformal transformation  induces an infinitesimal homothetic transformation on .  Furthermore,  the correspondence   gives a homomorphism of the Lie algebra of infinitesimal fiber-preserving conformal transformations on  onto the Lie algebra of infinitesimal ...

Let (M,ω) be a symplectic manifold of dimension 2n, and let J ∈ J (M,ω) be an ω-compatible almost complex structure. Let gJ(·, ·) ≡ ω(·, J ·) be the corresponding hermitian metric (i.e. J-invariant Riemannian metric) on M . Let (Σ, j) be a Riemann surface (not necessarily compact) with complex structure j. A smooth map u : Σ → M is called a (J, j)-holomorphic map (or simply a J-holomorphic map)...

The aim of the present paper is to characterize almost co-K?hler manifolds whose metrics are Riemann solitons. At first we provide a necessary and sufficient condition for metric 3-dimensional manifold be soliton. Next it proved that if an soliton with vector field ?, then flat. It also shown (?, ?)-almost ? < 0 soliton, expanding satisfies relation. We prove there does not exist gradient so...

Let M be a hyperbolic 3–manifold, namely a complete 3–dimensional Riemannian manifold of constant curvature −1, such that the fundamental group π1 (M) is finitely generated. A fundamental subset of M is its convex core CM , defined as the smallest non-empty closed convex subset ofM . The boundary ∂CM of this convex core is a surface of finite topological type, and its geometry was described by ...

Ricci-like solitons with arbitrary potential are introduced and studied on Sasaki-like almost contact B-metric manifolds. A manifold of this type can be considered as an complex Riemannian which cone is a holomorphic manifold. The soliton under study characterized proved that its Ricci tensor equal to the vertical component both B-metrics multiplied by constant. Thus, scalar curvatures respect ...