Constant isotropic submanifolds with 4-planar geodesics

Pak, Jin Suk; Sakamoto, Kunio

doi:10.1090/S0002-9947-1988-0936819-7

Constant isotropic submanifolds with $4$-planar geodesics
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by Jin Suk Pak and Kunio Sakamoto

Trans. Amer. Math. Soc. 307 (1988), 317-333

DOI: https://doi.org/10.1090/S0002-9947-1988-0936819-7

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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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