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Berger spheres are introduced by Marcel Berger. These are odd dimensional spheres, which are squashed in a direction. The shrinking direction can be provided by the circle action on the complex Euclidean space. In other words, it corresponds to shrinking or expanding the Hopf circles in an odd dimensonal sphere. Consequently, the resulting Riemannian metric is different than the round metric. In these seminar series, we understand the curvature and the Jacobi operator of  Berger spheres embedded in complex projective spaces.

We will be using the following resources.

References:

1. Kalafat, Kelekçi and Taşdemir. Minimal submanifolds and stability in Einstein manifolds. E-print available at arXiv:2406.03347. math.DG, 2024.