Scalar curvature of defineable CAT-spaces.
Second order connections on some functional bundles
We study the second order connections in the sense of C. Ehresmann. On a fibered manifold , such a connection is a section from into the second non-holonomic jet prolongation of . Our main aim is to extend the classical theory to the functional bundle of all smooth maps between the fibers over the same base point of two fibered manifolds over the same base. This requires several new geometric results about the second order connections on , which are deduced in the first part of the paper.
Second order differential invariants of linear frames.
Second variational derivative of local variational problems and conservation laws
We consider cohomology defined by a system of local Lagrangian and investigate under which conditions the variational Lie derivative of associated local currents is a system of conserved currents. The answer to such a question involves Jacobi equations for the local system. Furthermore, we recall that it was shown by Krupka et al. that the invariance of a closed Helmholtz form of a dynamical form is equivalent with local variationality of the Lie derivative of the dynamical form; we remark that...
Second-order conformally equivariant quantization in dimension .
Semilinear equations, the function, and generalized Gauduchon metrics
In this paper, we generalize the Gauduchon metrics on a compact complex manifold and define the functions on the space of its hermitian metrics.
Semi-rigid CR structures and holomorphic extendability
Separation, factorization and finite sheaves on Nash manifolds
Separation of variables in the problems of normal and compact solvability of the exterior derivation operator.
Seven-dimensional considerations of Einstein's connection. II: The recurrence relations of the second and third kind in 7--UFT.
Seven-dimensional considerations of Einstein's connection. I: The recurrence relations of the first kind in --UFT.
Seven-dimensional considerations of Einstein'sconnection. III: The seven-dimensional Einstein's connection.
Simple germs of corank one affine distributions
Simplicial types and polynomial algebras
This paper shows that the simplicial type of a finite simplicial complex is determined by its algebra of polynomial functions on the baricentric coordinates with coefficients in any integral domain. The link between and is done through certain admissible matrix associated to in a natural way. This result was obtained for the real numbers by I. V. Savel’ev [5], using methods of real algebraic geometry. D. Kan and E. Miller had shown in [2] that determines the homotopy type of the polyhedron...
Singular foliations and differential -forms
Singularités d'ordre supérieur de 1-formes, 2-formes et équations de Pfaff
Singularities and normal forms of generic 2-distributions on 3-manifolds
We give a complete classification of germs of generic 2-distributions on 3-manifolds. By a 2-distribution we mean either a module generated by two vector fields (at singular points its dimension decreases) or a Pfaff equation, i.e. a module generated by a differential 1-form (at singular points the dimension of its kernel increases).
Singularities and normal forms of smooth distributions
In this expository paper we present main results (from classical to recent) on local classification of smooth distributions.
Singularities of envelopes of families of submanifolds in