In this short survey, we would like to overview the recent development of the study on Deligne-Malgrange lattices and resolution of turning points for algebraic meromorphic flat bundles. We also explain their relation with wild harmonic bundles. The author hopes that it would be helpful for access to his work on wild harmonic bundles.
It was conjectured in [26] that, for all submanifolds of all real space forms , the Wintgen inequality is valid at all points of , whereby is the normalised scalar curvature of the Riemannian manifold and , respectively , are the squared mean curvature and the normalised scalar normal curvature of the submanifold in the ambient space , and this conjecture was shown there to be true whenever codimension . For a given Riemannian manifold , this inequality can be interpreted as follows:...
In this paper we continue the investigation of [7]-[10] concerning the actions of discrete subgroups of Lie groups on compact manifolds.
In this paper, we prove by using the minimax principle that there exist infinitely many -equivariant harmonic maps from a specific Lorentz manifold to a compact Riemannian manifold.
Using a generalization of [Pol] we present a description of complex geodesics in arbitrary complex ellipsoids.
In this note we introduce the concept of F-algebroid, and give its elementary properties and some examples. We provide a description of the almost duality for Frobenius manifolds, introduced by Dubrovin, in terms of a composition of two anchor maps of a unique cotangent F-algebroid.
A new definition for lifts and lowerings is given, linking the different tensor algebras involved in the usual treatment of Finsler manifolds. By means of them, the relation between the different classes of linear connections is made clearer.