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.

An algorithm based on rolling to generate smooth interpolating curves on ellipsoids

Krzysztof Krakowski, Fátima Silva Leite (2014)

Kybernetika

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We present an algorithm to generate a smooth curve interpolating a set of data on an n -dimensional ellipsoid, which is given in closed form. This is inspired by an algorithm based on a rolling and wrapping technique, described in [11] for data on a general manifold embedded in Euclidean space. Since the ellipsoid can be embedded in an Euclidean space, this algorithm can be implemented, at least theoretically. However, one of the basic steps of that algorithm consists in rolling the ellipsoid,...