[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.11568/kjm.2018.26.1.75

NONCONSTANT WARPING FUNCTIONS ON EINSTEIN WARPED PRODUCT MANIFOLDS WITH 2-DIMENSIONAL BASE

Lee, Soo-Young (Department of Mathematics Chosun University)

Publication Information

Korean Journal of Mathematics / v.26, no.1, 2018 , pp. 75-85 More about this Journal

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 $g=g_B+f(t)^2g_F$ . And we consider a 2-dimensional base manifold B with a metric $g_B=dt^2+(f^{\prime}(t))^2du^2$ . 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; scalar curvature; Einstein manifold; Ricci tensor; Ricci curvature;

Citations & Related Records

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