On 3-dimensional normal almost contact pseudo-metric manifolds
Tóm tắt
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
$$\beta $$
is harmonic, and if
$$\beta =0$$
on M, then the function
$$\alpha $$
is harmonic. Furthermore we give the necessary and sufficient condition for normal almost contact pseudo-metric 3-manifold to be
$$\beta $$
-Sasakian pseudo-metric manifold. Finally, we study the class of symmetric parallel (0, 2)-tensor field and its consequences.
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