Tohoku Mathematical Journal
2025
September
SECOND SERIES VOL. 77, NO. 3

Tohoku Math. J.
77 (2025), 345-356

Title REDEFINITION OF BERGER SPHERES FROM THE VIEWPOINT OF SUBMANIFOLD GEOMETRY

Dedicated to Professor Hiroshi Asano
Author Sadahiro Maeda and Hiromasa Tanabe

(Received February 27, 2023, revised August 3, 2023)
Abstract. We first investigate geometric properties of geodesic spheres with sufficiently big radii in a complex projective space. Motivated by this result, we redefine Berger spheres. Our aim is to study such Berger spheres from the viewpoints of contact geometry, submanifold geometry and length spectral geometry.

Mathematics Subject Classification. Primary 53B25, Secondary 53C40.
Key words and phrases. Berger spheres, complex projective spaces, geodesic spheres, Sasakian space forms, homogeneous submanifolds, parallel mean curvature vector, length spectrum.

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