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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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참고문헌 (11)
참고문헌 신청
A.L. Besse / 1987 / Einstein manifolds / Springer-Verlag
J.K. Beem / 1981 / Global Lorentzian geometry, Pure and Applied Mathematics, Vol. 67 / Dekker
J.K. Beem / 1996 / Global Lorentzian Geometry / Marcel Dekker, Inc
J. Case / 2011 / Rigidity of quasi-Einstein metrics / Diff. Geo. and its applications 29:93~100
F.E.S. Feitosa / 2017 / On the construction of gradient Ricci soliton warped product / math.DG. 26
J.K. Beem / 1981 / Global Lorentzian geometry, Pure and Applied Mathematics, Vol. 67 / Dekker
J.K. Beem / 1996 / Global Lorentzian Geometry / Marcel Dekker, Inc
J. Case / 2011 / Rigidity of quasi-Einstein metrics / Diff. Geo. and its applications 29:93~100
F.E.S. Feitosa / 2017 / On the construction of gradient Ricci soliton warped product / math.DG. 26
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