Abstract
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 (Formula presented.), 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.
Original language | English |
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Pages (from-to) | 2100-2110 |
Number of pages | 11 |
Journal | Mathematische Nachrichten |
Volume | 290 |
Issue number | 14-15 |
DOIs | |
Publication status | Published - Oct 2017 |
Bibliographical note
Publisher Copyright:© 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Keywords
- (m,ρ)-quasi Einstein manifold
- 53B15
- 53B20
- 53C21
- 53C25
- closed conformal vector field
- conformal mapping
- warped product