Displaying similar documents to “A characterization of the Grassmann manifold G p , 2 ( ℝ ) . Another review.”

On the energy of unit vector fields with isolated singularities

Fabiano Brito, Paweł Walczak (2000)

Annales Polonici Mathematici

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We consider the energy of a unit vector field defined on a compact Riemannian manifold M except at finitely many points. We obtain an estimate of the energy from below which appears to be sharp when M is a sphere of dimension >3. In this case, the minimum of energy is attained if and only if the vector field is totally geodesic with two singularities situated at two antipodal points (at the 'south and north pole').

Curvature properties of φ-null Osserman Lorentzian S-manifolds

Letizia Brunetti, Angelo Caldarella (2014)

Open Mathematics

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We expound some results about the relationships between the Jacobi operators with respect to null vectors on a Lorentzian S-manifold and the Jacobi operators with respect to particular spacelike unit vectors. We study the number of the eigenvalues of such operators on Lorentzian S-manifolds satisfying the φ-null Osserman condition, under suitable assumptions on the dimension of the manifold. Then, we provide in full generality a new curvature characterization for Lorentzian S-manifolds...