Pointwise Semi-Slant Semi-Riemannian Maps

Abstract

We use the first variational formula on the fibers to deduce the necessary and sufficient conditions for the harmonicity of pointwise semi-slant semi Riemannian maps, which are defined on Lorentzian para-Sasakian manifolds. We define the sets of Legendre, Hamiltonian and Harmonic variations for any fibre of the map. Moreover, we address the characterization theorem for pointwise semi-slant semi Riemannian maps from Lorentzian para Saskian manifold to a semi-Riemannian metric manifold by considering the vertical Reeb vector field and investigate the properties of totally umbilical fibers. Beside from the peculiarities of pointwise semi-slant semi Riemannian maps, geometry of the distributions associated with the map such as integrability and totally geodesicness are also studied. In the end, we discuss a number of examples illustrating the existence of such maps.