Advances in Pure Mathematics
Vol.07 No.11(2017), Article ID:80554,2 pages
10.4236/apm.2017.711039
Erratum to “Manifolds with Bakry-Emery Ricci Curvature Bounded Below”, Advances in Pure Mathematics, Vol. 6 (2016), 754-764
Issa Allassane Kaboye1, Bazanfaré Mahaman2
1Faculté de Sciences et Techniques, Université de Zinder, Zinder, Niger
2Département de Mathématiques et Informatique, Université Abdou Moumouni, Niamey, Niger
Copyright © 2017 by authors and Scientific Research Publishing Inc.
This work is licensed under the Creative Commons Attribution International License (CC BY 4.0).
http://creativecommons.org/licenses/by/4.0/
Received: August 24, 2016; Accepted: October 14, 2016; Published: October 17, 2016
The original online version of this article (Issa Allassane Kaboye, Bazanfaré Mahaman (2016) Manifolds with Bakry-Emery Ricci Curvature bounded below 6, 754-764. http://dx.doi.org/10.4236/apm.2016.611061 unfortunately contains a mistake. The author wishes to correct the errors.
Lemma 3.5. Let (M, g, e−fdvolg) be a complete smooth metric measure space with ; fix ; if there exists c so that then for
Proof
Let x be a point in M and let be a minimal geodesic joining p to x and be a parallel orthonormal vector fields along . Set .
By the second variation formula we have:
Hence
For all positive reals r and s, integrating this relation we have:
Therefore we have . Hence
which implies
and integrating from 0 to R' with respect to s we obtain the conclusion.