Automorphisms of differential groups
Automorphisms of spatial curves.
Automorphisms of spatial curves
Automorphisms of curves , in are investigated; i.e. invertible transformations, where the coordinates of the transformed curve , depend on the derivatives of the original one up to some finite order . While in the two-dimensional space the problem is completely resolved (the only possible transformations are the well-known contact transformations), the three-dimensional case proves to be much more complicated. Therefore, results (in the form of some systems of partial differential equations...
Automorphisms of submanifolds.
Banachian Differentiable Spaces.
Beispiele zur lokalen Theorie der differenzierbaren Räume.
Beschränkte Lösungen der Cauchy-Riemannschen Differentialgleichungen auf q-konkaven Gebieten.
Boundaries of graphs of harmonic functions.
Bounding the degree of solutions to Pfaff equations
We study hypersurfaces of complex projective manifolds which are invariant by a foliation, or more generally which are solutions to a Pfaff equation. We bound their degree using classical results on logarithmic forms.
Bundle functors on all foliated manifold morphisms have locally finite order
We prove that any bundle functor F:ℱol → ℱℳ on the category ℱ olof all foliated manifolds without singularities and all leaf respecting maps is of locally finite order.
Bundle functors with the point property which admit prolongation of connections
Let F:ℳ f →ℱℳ be a bundle functor with the point property F(pt) = pt, where pt is a one-point manifold. We prove that F is product preserving if and only if for any m and n there is an -canonical construction D of general connections D(Γ) on Fp:FY → FM from general connections Γ on fibred manifolds p:Y → M.
Calcul différentiel extérieur de dégré arbitraire.
Calculus of variations with differential forms
We study integrals of the form , where , is continuous and is a -form. We introduce the appropriate notions of convexity, namely ext. one convexity, ext. quasiconvexity and ext. polyconvexity. We study their relations, give several examples and counterexamples. We finally conclude with an application to a minimization problem.
Calibrated geometries in Grassmann manifolds.
Canonical 1-forms on higher order adapted frame bundles
Let be a foliated -dimensional manifold with -dimensional foliation . Let be a finite dimensional vector space over . We describe all canonical (-invariant) -valued -forms on the -th order adapted frame bundle of .
Canonical differential structures of regular covectors
Canonical equivariant extensions using classical Hodge theory.
Canonical form on a groupoid related to regular prolongations of Lie groups
Canonical nonlinear connections in the multi-time Hamilton geometry.
Canonical symplectic structures on the r-th order tangent bundle of a symplectic manifold.
We describe all canonical 2-forms Λ(ω) on the r-th order tangent bundle TrM = Jr0 (R;M) of a symplectic manifold (M, ω). As a corollary we deduce that all canonical symplectic structures Λ(ω) on TrM over a symplectic manifold (M, ω) are of the form Λ(ω) = Σrk=0 αkω(k) for all real numbers αk with αr ≠ 0, where ω(k) is the (k)-lift (in the sense of A. Morimoto) of ω to TrM.