It is very natural to consider the next case see Section 2. Now, we consider that the base is a noncompact Riemannian manifold.
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Considering a conformal structure for the base of an Einstein warped product semi-Riemannian manifold, we have the next results. The following theorem is very technical. In order, for the reader to have a more intimate view of the next results, we recommend a previous reading of Section 2. It is worth mentioning that the first item of Theorem 5 was not considered in [ 3 ].
From Theorem 5, we can construct examples of complete Einstein warped product Riemannian manifolds. The article is organized as follows.
- Regularity of Einstein manifolds and the codimension 4 conjecture;
-  Almost Einstein and Poincare-Einstein manifolds in Riemannian signature!
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Section 2 is divided in two subsections, namely, General formulas and A conformal structure for the warped product with Ricci-flat fibre , where will be provided the preliminary results. Further, in Section 3 , we will prove our main results. Then, from [ 5 ] the result follows.
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Now, consider the conformal structure given in Section 2. Therefore, from 2. From 2. Then, from 3. The authors would like to express their deep thanks to professor Ernani Ribeiro Jr for valuable suggestions. Finally, the author wants to thank the referee for his careful reading and helpful suggestions. Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide. Sign In or Create an Account.
Sign In. Advanced Search. Article Navigation. Close mobile search navigation Article Navigation. Volume 3. Article Contents.
Proof of the main results. On the structure of Einstein warped product semi-Riemannian manifolds Benedito Leandro. Corresponding author.
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Email: bleandroneto gmail. Oxford Academic. Google Scholar. Romildo Pina. Cite Citation. Permissions Icon Permissions. Communicated by: Maciej Dunajski.
We derive some useful formulae from system 2. Contracting the first equation of 2. Then, from 2.here
Essays on Einstein manifolds
When the base is a Riemannian manifold and the fibre is a Ricci-flat semi-Riemannian manifold i. We use the Lie theory of transformation groups to reduce the partial differential equations 2. In fact, from the third equation of the system 2. Therefore, from 3.
Moreover, from the third equation in 2. From 3. The first equation of 2. Above all, the book provides a clear insight into the scope and diversity of problems posed by its title. Salamon in MathSciNet This prophecy is indeed fulfilled. Wilmore in Bulletin of the London Mathematical Society Skip to main content Skip to table of contents. Advertisement Hide. Einstein Manifolds. Front Matter Pages i-xii.
Pages Basic Material. Riemannian Functionals.
Ricci Curvature as a Partial Differential Equation.