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Distance spheres in complex projective spaces
Author:
Alan Weinstein
Journal:
Proc. Amer. Math. Soc. 39 (1973), 649-650
MSC:
Primary 53C20
Erratum:
Proc. Amer. Math. Soc. 48 (1975), 519.
MathSciNet review:
0315631
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Abstract: Distance spheres in complex projective spaces are counterexamples to the odd-dimensional extension of a lemma of Klingenberg.
- [1]
M. Berger, On the diameter of some Riemannian manifolds, Technical Report, University of California, Berkeley, 1962.
- [2]
Isaac
Chavel, A class of Riemannian homogeneous spaces, J.
Differential Geometry 4 (1970), 13–20. MR 0270295
(42 #5185)
- [3]
Detlef
Gromoll, Differenzierbare Strukturen und Metriken positiver
Krümmung auf Sphären, Math. Ann. 164
(1966), 353–371 (German). MR 0196754
(33 #4940)
- [4]
W.
Klingenberg, Contributions to Riemannian geometry in the
large, Ann. of Math. (2) 69 (1959), 654–666. MR 0105709
(21 #4445)
- [5]
Wilhelm
Klingenberg, Über Riemannsche Mannigfaltigkeiten mit positiver
Krümmung, Comment. Math. Helv. 35 (1961),
47–54 (German). MR 0139120
(25 #2559)
- [6]
Wilhelm
Klingenberg, Über Riemannsche Mannigfaltigkeiten mit nach oben
beschränkter Krümmung, Ann. Mat. Pura Appl. (4)
60 (1962), 49–59 (German). MR 0157321
(28 #556)
- [1]
- M. Berger, On the diameter of some Riemannian manifolds, Technical Report, University of California, Berkeley, 1962.
- [2]
- I. Chavel, A class of Riemannian homogeneous spaces, J. Differential Geometry 4 (1970), 13-20. MR 42 #5185. MR 0270295 (42:5185)
- [3]
- D. Gromoll, Differenzierbare Strukturen und Metriken positiver Krümmung auf Sphären, Math. Ann. 164 (1966), 353-371. MR 33 #4940. MR 0196754 (33:4940)
- [4]
- W. Klingenberg, Contributions to Riemannian geometry in the large, Ann. of Math. (2) 69 (1959), 654-666. MR 21 #4445. MR 0105709 (21:4445)
- [5]
- -, Über Riemannsche Mannigfaltigkeiten mit positiver Krümmung, Comment. Math. Helv. 35 (1961), 47-54. MR 25 #2559. MR 0139120 (25:2559)
- [6]
- -, Über Riemannsche Mannigfaltigkeiten mit nach oben beschrankter Krümmung, Ann. Mat. Pura Appl. (4) 60 (1962), 49-59. MR 28 #556. MR 0157321 (28:556)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9939-1973-0315631-0
PII:
S 0002-9939(1973)0315631-0
Keywords:
Complex projective space,
geodesics,
sectional curvature
Article copyright:
© Copyright 1973 American Mathematical Society
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