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Curvature of hyperkähler quotients

Roger Bielawski (2008)

Open Mathematics

We prove estimates for the sectional curvature of hyperkähler quotients and give applications to moduli spaces of solutions to Nahm’s equations and Hitchin’s equations.

Curvature properties of a semi-symmetric metric connection on S-manifolds

Mehmet Akif Akyol, Aysel Turgut Vanli, Luis M. Fernández (2013)

Annales Polonici Mathematici

In this study, S-manifolds endowed with a semi-symmetric metric connection naturally related with the S-structure are considered and some curvature properties of such a connection are given. In particular, the conditions of semi-symmetry, Ricci semi-symmetry and Ricci-projective semi-symmetry of this semi-symmetric metric connection are investigated.

Curvature properties of φ-null Osserman Lorentzian S-manifolds

Letizia Brunetti, Angelo Caldarella (2014)

Open Mathematics

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 and we use...

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