Korean J. Math. Vol. 26 No. 1 (2018) pp.75-85
DOI: https://doi.org/10.11568/kjm.2018.26.1.75

Nonconstant warping functions on Einstein warped product manifolds with $2-$dimensional base

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Published: Mar 30, 2018
Keywords:
warping function, warped product manifold, Einstein manifold
Mathematics Subject Classification:
53C15, 53C21, 53C25, 58D17

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

Abstract

In this paper, we study nonconstant warping functions on an Einstein warped product manifold $M=B \times _{f^2} F$ with a warped product metric $g=g_B +f(t)^2 g_F$. And we consider a $2-$dimensional base manifold $B$~ with a metric $g_B = dt^2 +(f'(t))^2 du^2 .$ As a result, we prove the following: if $M$ is an Einstein warped product manifold with a $2-$dimensional base, then there exist generally nonconstant warping functions $f(t).$


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