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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Constant isotropic submanifolds with $ 4$-planar geodesics

Authors: Jin Suk Pak and Kunio Sakamoto
Journal: Trans. Amer. Math. Soc. 307 (1988), 317-333
MSC: Primary 53C40
MathSciNet review: 936819
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Abstract: Let $ f$ be an isometric immersion of a Riemannian manifold $ M$ into $ \overline M $. We prove that if $ f$ is constant isotropic, $ 4$-planar geodesic and $ \overline M $ is a Euclidean sphere, then $ M$ is isometric to one of compact symmetric spaces of rank equal to one and $ f$ is congruent to a direct sum of standard minimal immersions. We also determine constant isotropic, $ 4$-planar geodesic, totally real immersions into a complex projective space of constant holomorphic sectional curvature.

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Keywords: Second fundamental forms, isotropic and $ 4$-planar geodesic immersions, totally real immersions
Article copyright: © Copyright 1988 American Mathematical Society