Rigidity of Einstein manifolds and generalized quasi-Einstein manifolds

Deng, Yi Hua; Luo, Li; Zhou, Li

doi:10.4064/ap115-3-3

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Definition 11 ([21]) a Riemannian Manifold (1

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“…Also, in [18], Filho has investigated the Einstein warped products endowed with a parallel vector fields. Moreover, in [15] Deng et.al. has obtained some rigidity results of Einstein and generalized quasi Einstein manifolds.…”

Section: Definition 11 ([21]) a Riemannian Manifold (mentioning

confidence: 99%

Rigidity of (m,ρ)-quasi Einstein manifolds

Demirbağ

Güler

2017

Math. Nachr.

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This paper deals with the study on (m,ρ)‐quasi Einstein manifolds. First, we give some characterizations of an (m,ρ)‐quasi Einstein manifold admitting closed conformal or parallel vector field. Then, we obtain some rigidity conditions for this class of manifolds. We prove that an (m,ρ)‐quasi Einstein manifold with a closed conformal vector field has a warped product structure of the form I×eq/2M∗, where I is a real interval, (M∗,g∗) is an (n−1)‐dimensional Riemannian manifold and q is a smooth function on I. Finally, a non‐trivial example of an (m,ρ)‐quasi Einstein manifold verifying our results in terms of the potential function is presented.

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Section: Definition 11 ([21]) a Riemannian Manifold (mentioning

confidence: 99%