Curvature estimates for minimal surfaces in -manifolds
Prompted by recent work of Xiuxiong Chen, a unified approach to the Hamilton-Ricci and Calabi flows on a closed, compact surface is presented, recovering global existence and exponentially fast asymptotic convergence from concentration-compactness results for conformal metrics.
Curvature homogeneity of (torsion-free) affine connections on manifolds is an adaptation of a concept introduced by I. M. Singer. We analyze completely the relationship between curvature homogeneity of higher order and local homogeneity on two-dimensional manifolds.
We study curvature homogeneous spaces or locally homogeneous spaces whose curvature tensors are invariant by the action of “large" Lie subalgebras of . In this paper we deal with the cases of
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.
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.