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 ...

the mathematical aspect of cartographic mapping is a process which establishes a unique connection between points of the earth’s sphere and their images on a plane. it was proven in differential geometry that an isometric mapping of a sphere onto a plane with all corresponding distances on both surfaces remaining identical can never be achieved since the two surfaces do not possess the same gau...

The continuous extension of the discrete duality symmetry of the SchwarzSen model is studied. The corresponding infinitesimal generator Q turns out to be local, gauge invariant and metric independent. Furthermore, Q commutes with all the conformal group generators. We also show that Q is equivalent to the non—local duality transformation generator found in the Hamiltonian formulation of Maxwell...

The continuous extension of the discrete duality symmetry of the SchwarzSen model is studied. The corresponding infinitesimal generator Q turns out to be local, gauge invariant and metric independent. Furthermore, Q commutes with all the conformal group generators. We also show that Q is equivalent to the non—local duality transformation generator found in the Hamiltonian formulation of Maxwell...

In this paper, we construct a bialgebra theory for associative conformal algebras, namely antisymmetric infinitesimal bialgebras. On the one hand, it is an attempt to give structures other under certain conditions, such are equivalent double constructions of Frobenius which algebras that decomposed into direct sum another algebra and its dual as C[∂]-modules both them subalgebras natural biline...

This paper belongs to the realm of conformal geometry and deals with Euclidean submanifolds that admit smooth variations are infinitesimally conformal. Conformal a classical subject in differential geometry. In fact, already 1917 Cartan classified parametrically hypersurfaces nontrivial variations. Our first main result is Fundamental theorem for infinitesimal The second rigidity lie low codime...