ON STABILITY OF EINSTEIN WARPED PRODUCT MANIFOLDS Pyo, Yong-Soo; Kim, Hyun-Woong; Park, Joon-Sik;
Let (B, ) and (N, ) be Einstein manifolds. Then, we get a complete (necessary and sufficient) condition for the warped product manifold ) to be Einstein, and obtain a complete condition for the Einstein warped product manifold to be weakly stable. Moreover, we get a complete condition for the map i : (, which is the identity map as a map, to be harmonic. Under the assumption that i is harmonic, we obtain a complete condition for to be Einstein.
harmonic map;stability of harmonic map;warped product manifold;
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