Geometry of conformal vector fields

construction of vector fields with positive lyapunov exponents

in this thesis our aim is to construct vector field in r3 for which the corresponding one-dimensional maps have certain discontinuities. two kinds of vector fields are considered, the first the lorenz vector field, and the second originally introced here. the latter have chaotic behavior and motivate a class of one-parameter families of maps which have positive lyapunov exponents for an open in...

Computational Conformal Geometry Applied in Engineering Fields

Computational conformal geometry is an interdisciplinary field, combining modern geometry theories from pure mathematics with computational algorithms from computer science. Computational conformal geometry offers many powerful tools to handle a broad range of geometric problems in engineering fields. This work summarizes our research results in the past years. We have introduced efficient and ...

Conformal Vector Fields in Symmetric and Conformal Symmetric Spaces

Consequences of the existence of conformal vector fields in (locally) symmetric and conformal symmetric spaces, have been obtained. An attempt has been made for a physical interpretation of the consequences in the framework of general relativity.

Conformal vector fields and conformal transformations on a Riemannian manifold

In this paper first it is proved that if ξ is a nontrivial closed conformal vector field on an n-dimensional compact Riemannian manifold (M, g) with constant scalar curvature S satisfying S ≤ λ1(n − 1), λ1 being first nonzero eigenvalue of the Laplacian operator ∆ on M and Ricci curvature in direction of a certain vector field is non-negative, then M is isometric to the n-sphere S(c), where S =...

Zeros of Conformal Vector Fields and Twistor Spinors in Lorentzian Geometry