LAUSR

The purpose of this paper is to study the almost contact pseudo-metric manifolds of dimension three which are normal. We derive certain necessary and sufficient conditions for an almost contact pseudo-metric manifold to be normal. We prove that in a normal almost contact pseudo-metric 3-manifold M of constant curvature k the function $$\beta $$ β is harmonic, and if $$\beta =0$$ β = 0 on M , then the function $$\alpha $$ α is harmonic. Furthermore we give the necessary and sufficient condition for normal almost contact pseudo-metric 3-manifold to be $$\beta $$ β -Sasakian pseudo-metric manifold. Finally, we study the class of symmetric parallel (0, 2)-tensor field and its consequences.