TY - JOUR
T1 - The nonuniqueness of the tangent cones at infinity of Ricci-flat manifolds
AU - Hattori, Kota
N1 - Funding Information:
Acknowledgments The author would like to thank Professor Shouhei Honda who invited the author to this attractive topic, and also for advice on this paper. The author also would like to thank the referee for careful reading and several useful comments. Thanks to these, the author could make the main results much stronger. The author was supported by Grant-in-Aid for Young Scientists (B) Grant Number 16K17598. The author was partially supported by JSPS Core-to-Core Program, “Foundation of a Global Research Cooperative Center in Mathematics focused on Number Theory and Geometry”.
Publisher Copyright:
© 2017, Mathematical Sciences Publishers. All rights reserved.
PY - 2017/8/15
Y1 - 2017/8/15
N2 - Colding and Minicozzi established the uniqueness of the tangent cones at infinity of Ricci-flat manifolds with Euclidean volume growth where at least one tangent cone at infinity has a smooth cross section. In this paper, we raise an example of a Ricci-flat manifold implying that the assumption for the volume growth in the above result is essential. More precisely, we construct a complete Ricci-flat manifold of dimension 4 with non-Euclidean volume growth that has infinitely many tangent cones at infinity where one of them has a smooth cross section.
AB - Colding and Minicozzi established the uniqueness of the tangent cones at infinity of Ricci-flat manifolds with Euclidean volume growth where at least one tangent cone at infinity has a smooth cross section. In this paper, we raise an example of a Ricci-flat manifold implying that the assumption for the volume growth in the above result is essential. More precisely, we construct a complete Ricci-flat manifold of dimension 4 with non-Euclidean volume growth that has infinitely many tangent cones at infinity where one of them has a smooth cross section.
UR - http://www.scopus.com/inward/record.url?scp=85028314837&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85028314837&partnerID=8YFLogxK
U2 - 10.2140/gt.2017.21.2683
DO - 10.2140/gt.2017.21.2683
M3 - Article
AN - SCOPUS:85028314837
SN - 1465-3060
VL - 21
SP - 2683
EP - 2723
JO - Geometry and Topology
JF - Geometry and Topology
IS - 5
ER -