Rigidity of (m,ρ)‐quasi Einstein manifolds

Rigidity of (m,ρ)‐quasi Einstein manifolds

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 Einstei...

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Veröffentlicht in:Mathematische Nachrichten 2017-10, Vol.290 (14-15), p.2100-2110
Hauptverfasser: Altay Demirba, Sezgin, Guler, Sinem
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Sprache:eng
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(m,ρ)‐quasi Einstein manifold
53B15
53B20
53C21
53C25
closed conformal vector field
conformal mapping
Production planning
Riemann manifold
Rigidity
warped product
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Guler, Sinem
description 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.
doi_str_mv 10.1002/mana.201600186
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subjects (m,ρ)‐quasi Einstein manifold
53B15
53B20
53C21
53C25
closed conformal vector field
conformal mapping
Production planning
Riemann manifold
Rigidity
warped product
title Rigidity of (m,ρ)‐quasi Einstein manifolds
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