Length spectrum of geodesic spheres in a non-flat complex space form

Trajectories on Geodesic Spheres in a Non-Flat Complex Space Form

“…On the other hand, by Lemmas 1.1 and 1.2 in [6], for unit tangent vectors u ∈ T x M and v ∈ T y M which are orthogonal to ξ x and ξ y respectively, we have isometries…”

“…[6]): Proposition 2. The extrinsic shape of a trajectory γ with ρ γ = ±1 for a canonical magnetic field F κ on a real hypersurface M of type A is a trajectory for a Kähler magnetic field B ±ν(M ;c) on M n (c; C).…”

CHARACTERIZATIONS OF HYPERSURFACES OF TYPE A2 IN A COMPLEX PROJECTIVE SPACE

“…Hypersurfaces of type A 1 have two distinct constant principal curvatures in CP n . It is well known that CP n does not admit totally umbilic real hypersurfaces and that a real hypersurface M 2n−1 in CP n (n 3) is of type A 1 if and only if M has at most two distinct principal curvatures at each point of M. These tell us that 2 S. Maeda and T. Adachi [2] hypersurfaces of type A 1 are the simplest examples of real hypersurfaces in CP n . Hypersurfaces of type A 2 have three distinct constant principal curvatures in CP n .…”

“…. , k d−1 satisfying the following system of ordinary differential equations: Extrinsic shapes of geodesics were studied in the preceding papers [1,2].…”

“…LEMMA 4.1 (Adachi et al [2]). Let γ be a geodesic with structure torsion ρ γ on a hypersurface M of type A 1 with radius r (0 < r < π/2) in CP n .…”