Jacobi fields and its application of normal contact Lorentzian manifolds (Q5952802)

The properties of odd-dimensional manifolds with normal contact Lorentzian structure are studied. One considers manifolds of constant \(\varphi \)-sectional curvature. The Jacobi fields of such manifolds with respect to space-like geodesics are found and their characterization by means of geodesic spheres is given. For these purposes the author uses the Jacobi fields with respect to the structure vector field \(\xi \), i.e. the geodesics are integrable curves of \(\xi \). Methods of obtaining the Jacobi fields with respect to time-like geodesics are also suggested.