Korean J. Math. Vol. 27 No. 4 (2019) pp.1133-1147
DOI: https://doi.org/10.11568/kjm.2019.27.4.1133

Some metric on Einstein Lorentzian warped product manifolds

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Published: Dec 30, 2019
Keywords:
Einstein manifold, Lorentzian warped product manifold, geodesic, warping function, multiply warped product
Mathematics Subject Classification:
53C25, 53C50, 58E10, 53C21, 58D17

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Soo-Young Lee
Department of Mathematics Chosun University, Kwangju, 61452, Republic of Korea.

Abstract

In this paper, let $M=B \times_{f^2} F$ be an Einstein Lorentzian warped product manifold with $2-$dimensional base. We study the geodesic completeness of some metric with constant curvature. First of all, we discuss the existence of nonconstant warping functions on $M.$ As the results, we have some metric $g$ admits nonconstant warping functions $f.$ Finally, we consider the geodesic completeness on $M.$


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