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

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

Soo-Young Lee

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 $f(t).$

Keywords


warping function, warped product manifold, Einstein manifold

Subject classification

53C15, 53C21, 53C25, 58D17

Sponsor(s)



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