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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A Kähler deformation of $\textbf {C}\textrm {P}^ n$
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by H. Mori and Y. Watanabe PDF
Proc. Amer. Math. Soc. 103 (1988), 910-912 Request permission

Abstract:

We shall construct a one-parameter family of complete Kähler metrics on the $n$-dimensional complex projective space $C{P^n}$, including the Fubini-study metric. We shall get, as a corollary, many noncanonical $S{C^m}$ Kähler structures on $C{P^n}$.
References
  • Arthur L. Besse, Manifolds all of whose geodesics are closed, Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas], vol. 93, Springer-Verlag, Berlin-New York, 1978. With appendices by D. B. A. Epstein, J.-P. Bourguignon, L. Bérard-Bergery, M. Berger and J. L. Kazdan. MR 496885, DOI 10.1007/978-3-642-61876-5
  • Shoshichi Kobayashi and Katsumi Nomizu, Foundations of differential geometry. Vol I, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1963. MR 0152974
  • H. Mori and Y. Watanabe, Remarks on geodesics in a compact rotationally symmetric manifold, preprint.
  • Yoshiyuki Watanabe, Unitary-symmetric Kählerian manifolds and pointed Blaschke manifolds, Tsukuba J. Math. 12 (1988), no. 1, 129–148. MR 949906, DOI 10.21099/tkbjm/1496160640
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 103 (1988), 910-912
  • MSC: Primary 53C55; Secondary 32G05, 32J99
  • DOI: https://doi.org/10.1090/S0002-9939-1988-0947680-4
  • MathSciNet review: 947680