Riemannian manifolds admitting an infinitesimal conformal transformation

Riemannian Manifolds Admitting Isometric Immersions by Their First Eigenfunctions

Given a compact manifold M, we prove that every critical Riemannian metric g for the functional “first eigenvalue of the Laplacian” is λ1-minimal (i.e., (M, g) can be immersed isometrically in a sphere by its first eigenfunctions) and give a sufficient condition for a λ1-minimal metric to be critical. In the second part, we consider the case where M is the 2dimensional torus and prove that the ...

On Infinitesimal Conformal Transformations of the Tangent Bundles with the Generalized Metric

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 ...

An Infinite Family of Distinct 7-manifolds Admitting Positively Curved Riemannian Structures

On Riemannian manifolds endowed with a locally conformal cosymplectic structure

We deal with a locally conformal cosymplectic manifoldM(φ,Ω,ξ,η,g) admitting a conformal contact quasi-torse-forming vector field T . The presymplectic 2-form Ω is a locally conformal cosymplectic 2-form. It is shown that T is a 3-exterior concurrent vector field. Infinitesimal transformations of the Lie algebra of ∧M are investigated. The Gauss map of the hypersurfaceMξ normal to ξ is conforma...

Stretch fast dynamo mechanism via conformal mapping in Riemannian manifolds

Two new analytical solutions of self-induction equation, in Riemannian manifolds are presented. The first represents a twisted magnetic flux tube or flux rope in plasma astrophysics, which shows that the depending on rotation of the flow the poloidal field is amplified from toroidal field which represents a dynamo. The value of the amplification depends on the Frenet torsion of the magnetic axi...