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Characterizations of quasi-Einstein manifolds. (English) Zbl 1199.53078

Summary: We characterize here the quasi–Einstein manifolds by generalizing the characterizations of Einstein manifolds given for even dimension by B. Y. Chen, F. Dillen, L. Verstraelen and L. Vrancken in [Proc. Am. Math. Soc. 128, No. 2, 589–598 (2000; Zbl 1007.53019)] and for odd dimension by D. Dumitru [Bul. Univ. Transilvania Braşov, (to appear)].

MSC:

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53B20 Local Riemannian geometry
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)

Citations:

Zbl 1007.53019
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