Lie algebra of foliation preserving vector fields

On the Lie Algebra of a Transversally Complete Foliation

Harmonicity and Minimality of Vector Fields on Lorentzian Lie Groups

‎We consider four-dimensional lie groups equipped with‎ ‎left-invariant Lorentzian Einstein metrics‎, ‎and determine the harmonicity properties ‎of vector fields on these spaces‎. ‎In some cases‎, ‎all these vector fields are critical points for the energy functional ‎restricted to vector fields‎. ‎We also classify vector fields defining harmonic maps‎, ‎and calculate explicitly the energy of t...

Lie algebras of vector fields

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The Lie Algebra of Local Killing Fields

!We present an algebraic procedure that finds the Lie algebra of the local Killing fields of a smooth metric. In particular, we determine the number of independent local Killing fields about a given point on the manifold. As an application, we provide a local classification of the types of surfaces that admit the various possible Lie algebras of local Killing fields, in terms of the Gaussian cu...

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...