On some Ricci-flat metrics of cohomogeneity two on complex line bundles.
On some sheaves over a differential space
On "special" fibred coordinates for general and classical connections
Using a general connection Γ on a fibred manifold p:Y → M and a torsion free classical linear connection ∇ on M, we distinguish some “special” fibred coordinate systems on Y, and then we construct a general connection on Fp:FY → FM for any vector bundle functor F: ℳ f → of finite order.
On special types of nonholonomic -jets
We deduce a classification of all special types of nonholonomic -jets. In the introductory part, we summarize the basic properties of nonholonomic -jets.
On special types of nonholonomic jets
On special types of semiholonomic -jets
First we summarize some properties of the nonholonomic -jets from the functorial point of view. In particular, we describe the basic properties of our original concept of nonholonomic -jet category. Then we deduce certain properties of the Weil algebras associated with nonholonomic -jets. Next we describe an algorithm for finding the nonholonomic -jet categories. Finally we classify all special types of semiholonomic -jets.
On stable currents in positively pinched curved hypersurfaces
Let Mⁿ (n ≥ 3) be an n-dimensional complete hypersurface in a real space form N(c) (c ≥ 0). We prove that if the sectional curvature of M satisfies the following pinching condition: , where δ = 1/5 for n ≥ 4 and δ = 1/4 for n = 3, then there are no stable currents (or stable varifolds) in M. This is a positive answer to the well-known conjecture of Lawson and Simons.
On sufficiency of decomposable jets in
On super (or pseudo) differential forms as superfunctions
On symmetrization of jets
Let and be fiber product preserving bundle functors on the category of fibred manifolds with -dimensional bases and fibred maps covering local diffeomorphisms. We define a quasi-morphism to be a -invariant algebra homomorphism with . The main result is that there exists an -natural transformation depending on a classical linear connection on the base of if and only if there exists a quasi-morphism . As applications, we study existence problems of symmetrization (holonomization)...
On Tanaka's prolongation procedure for filtered structures of constant type.
On the algebraic structure on the jet prolongations of fibred manifolds
On the automorphisms of principal fibre bundles
On the classification of complex analytic supermanifolds.
On the cohomology sequence in a semiabelian category.
On the compactness theorem for differential forms.
On the complex of Sobolev spaces associated with an abstract Hilbert complex.
On the Connections on the Prolongations of Principal Fibre Bundles
On the Darboux transformation. II.
Automorphisms of the family of all Sturm-Liouville equations are investigated. The classical Darboux transformation arises as a particular case of a general result.
On the degree of C...-determinacy.