Tsukuba Journal of Mathematics

Metric spheres in the projective spaces with constant holomorphic sectional curvature

Nobuhiro Innami, Yukihiro Mashiko, and Katsuhiro Shiohama

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Abstract

We discuss codimension one isometric immersions of complete Riemannian manifolds into the projective spaces with constant holomorphic sectional curvature. Here, the shape operator and the curvature transformation with respect to the normal unit have the same eigenspaces. We then characterize the metric spheres in terms of the shape operator.

Article information

Source
Tsukuba J. Math., Volume 35, Number 1 (2011), 79-90.

Dates
First available in Project Euclid: 19 July 2011

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1311081450

Digital Object Identifier
doi:10.21099/tkbjm/1311081450

Mathematical Reviews number (MathSciNet)
MR2848817

Zentralblatt MATH identifier
1227.53064

Citation

Innami, Nobuhiro; Mashiko, Yukihiro; Shiohama, Katsuhiro. Metric spheres in the projective spaces with constant holomorphic sectional curvature. Tsukuba J. Math. 35 (2011), no. 1, 79--90. doi:10.21099/tkbjm/1311081450. https://projecteuclid.org/euclid.tkbjm/1311081450


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