Displaying similar documents to “Jacobi operator for leaf geodesics”

Stability of the geodesic flow for the energy

Eric Boeckx, José Carmelo González-Dávila, Lieven Vanhecke (2002)

Commentationes Mathematicae Universitatis Carolinae

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We study the stability of the geodesic flow ξ as a critical point for the energy functional when the base space is a compact orientable quotient of a two-point homogeneous space.

Normally flat semiparallel submanifolds in space forms as immersed semisymmetric Riemannian manifolds

Ülo Lumiste (2002)

Commentationes Mathematicae Universitatis Carolinae

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By means of the bundle of orthonormal frames adapted to the submanifold as in the title an explicit exposition is given for these submanifolds. Two theorems give a full description of the semisymmetric Riemannian manifolds which can be immersed as such submanifolds. A conjecture is verified for this case that among manifolds of conullity two only the planar type (in the sense of Kowalski) is possible.