Differential complex associated to closed differential forms of nonconstant rank.
Differential equations on contact riemannian manifolds
Differential forms as spinors
Differential forms, Weitzenböck formulae and foliations.
The Weitzenböck formulae express the Laplacian of a differential form on an oriented Riemannian manifold in local coordinates, using the covariant derivatives of the form and the coefficients of the curvature tensor. In the first part, we shall describe a certain "differential algebra formalism" which seems to be a more natural frame for those formulae than the usual calculations in local coordinates.In this formalism there appear some interesting differential operators which may also be used to...
Differential geometric structures of stable state feedback systems with dual connections
Differential geometrical relations for a class of formal series
An extension of the category of local manifolds is considered. Instead of smooth mappings of neighbourhoods of linear spaces as morphisms we deal with formal operator power series (or formal maps). Analogues of the objects appearing on smooth manifolds and vector bundles (vector fields, sections of a bundle, exterior forms, the de Rham complex, connection, etc.) are considered in this way. All the examinations are carried out in algebraic language, for we do not care about the convergence of formal...
Differential geometry of canonical quantization
Differential geometry of Cartan domains of type four
In this note we compute the sectional curvature for the Bergman metric of the Cartan domain of type IV and we give a classification of complex totally geodesic manifolds for this metric.
Differential Geometry of Complex Projective Space Curves.
Differential geometry of geodesic spheres.
Differential geometry of grassmannians and the Plücker map
Using the Plücker map between grassmannians, we study basic aspects of classic grassmannian geometries. For ‘hyperbolic’ grassmannian geometries, we prove some facts (for instance, that the Plücker map is a minimal isometric embedding) that were previously known in the ‘elliptic’ case.
Differential geometry of indefinite complex submanifolds in indefinite complex space forms.
Differential geometry of quaternionic manifolds
Differential Geometry of Real Monge-Ampère Foliations.
Differential Geometry of Real Submanifolds in a Kähler Manifold.
Differential geometry of surfaces
Differential geometry over the structure sheaf: a way to quantum physics
An idea for quantization by means of geometric observables is explained, which is a kind of the sheaf theoretical methods. First the formulation of differential geometry by using the structure sheaf is explained. The point of view to get interesting noncommutative observable algebras of geometric fields is introduced. The idea is to deform the algebra by suitable interaction structures. As an example of such structures the Poisson-structure is mentioned and this leads naturally to deformation...
Differential Inequlities on Complete Riemannian Manifolds and Applications.
Differential invariants of conformal and projective surfaces.
Differential invariants of the transformation group of a homogeneous space.