TY - JOUR
T1 - Differentiable sphere theorems whose comparison spaces are standard spheres or exotic ones
AU - Kondo, Kei
AU - Tanaka, Minoru
N1 - Funding Information:
Acknowledgements. In this work the first named author was supported by the JSPS KAKENHI Grant Numbers 17K05220, and partially 16K05133, 18K03280.
Publisher Copyright:
© 2020, Tokyo Institute of Technology. All rights reserved.
PY - 2020
Y1 - 2020
N2 - We show that for an arbitrarily given closed Riemannian manifold M admitting a point p ∊ M with a single cut point, every closed Riemannian manifold N admitting a point q ∊ N with a single cut point is diffeomorphic to M if the radial curvatures of N at q are sufficiently close in the sense of L1-norm to those of M at p.
AB - We show that for an arbitrarily given closed Riemannian manifold M admitting a point p ∊ M with a single cut point, every closed Riemannian manifold N admitting a point q ∊ N with a single cut point is diffeomorphic to M if the radial curvatures of N at q are sufficiently close in the sense of L1-norm to those of M at p.
KW - Bi-Lipschitz homeomorphism
KW - Differentiable sphere theorem
KW - Exotic spheres
KW - Radial curvature
KW - The Blaschke conjecture for spheres
KW - The Cartan-Ambrose-Hicks theorem
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U2 - 10.2996/kmj/1594313558
DO - 10.2996/kmj/1594313558
M3 - Article
AN - SCOPUS:85087843085
SN - 0386-5991
VL - 43
SP - 349
EP - 365
JO - Kodai Mathematical Journal
JF - Kodai Mathematical Journal
IS - 2
ER -