The geometrical interpretation of temporal cone norm in almost Minkowski manifold.
The geometry and conformal structure of properly embedded minimal surfaces of finite topology in IR3.
The geometry and spectrum of the one holed torus.
The geometry and topology of 3-Sasakian manifolds.
The geometry of a closed form
It is proved that a closed r-form ω on a manifold M defines a cohomology (called ω-coeffective) on M. A general algebraic machinery is developed to extract some topological information contained in the ω-coeffective cohomology. The cases of 1-forms, symplectic forms, fundamental 2-forms on almost contact manifolds, fundamental 3-forms on -manifolds and fundamental 4-forms in quaternionic manifolds are discussed.
The geometry of a semi-direct extension of a Heisenberg type nilpotent group
The geometry of a vector bundle endowed with a cone field.
The geometry of autonomous metrical multi-time Lagrange space of electrodynamics.
The geometry of closed hypersurfaces
The geometry of dented pentagram maps
We propose a new family of natural generalizations of the pentagram map from 2D to higher dimensions and prove their integrability on generic twisted and closed polygons. In dimension there are such generalizations called dented pentagram maps, and we describe their geometry, continuous limit, and Lax representations with a spectral parameter. We prove algebraic-geometric integrability of the dented pentagram maps in the 3D case and compare the dimensions of invariant tori for the dented maps...
The Geometry of Differential Harnack Estimates
In this short note, we hope to give a rapid induction for non-experts into the world of Differential Harnack inequalities, which have been so influential in geometric analysis and probability theory over the past few decades. At the coarsest level, these are often mysterious-looking inequalities that hold for ‘positive’ solutions of some parabolic PDE, and can be verified quickly by grinding out a computation and applying a maximum principle. In this note we emphasise the geometry behind the Harnack...
The geometry of nilpotent coadjoint orbits of convex type in hermitian Lie algebras.
The geometry of null systems, Jordan algebras and von Staudt's theorem
We characterize an important class of generalized projective geometries by the following essentially equivalent properties: (1) admits a central null-system; (2) admits inner polarities: (3) is associated to a unital Jordan algebra. These geometries, called of the first kind, play in the category of generalized projective geometries a rôle comparable to the one of the projective line in the category of ordinary projective geometries. In this general set-up, we prove an analogue of von Staudt’s...
The Geometry of Periodic Minimal Surfaces.
The geometry of pseudo harmonic morphisms.
The geometry of -covered foliations.
The geometry of the dual of a vector bundle.
The geometry of the moduli space of CP2 instantons.
The geometry of the space of Cauchy data of nonlinear PDEs
First-order jet bundles can be put at the foundations of the modern geometric approach to nonlinear PDEs, since higher-order jet bundles can be seen as constrained iterated jet bundles. The definition of first-order jet bundles can be given in many equivalent ways - for instance, by means of Grassmann bundles. In this paper we generalize it by means of flag bundles, and develop the corresponding theory for higher-oder and infinite-order jet bundles. We show that this is a natural geometric framework...
The global structure of constant mean curvature surfaces.