On the index theorem for symplectic orbifolds
We give an explicit construction of the trace on the algebra of quantum observables on a symplectiv orbifold and propose an index formula.
On the induced geometric object on submanifolds of homogeneous spaces
On the infinitesimal geometric objects of submanifolds
On the Initial-Boundary Value Problem for Harmonic Maps from the 2-Dimensional Minkowski Space.
On the Instability of Minimal Submanifolds in Riemannian Manifolds of Positive Curvature.
On the integrability of a -conformal Killing equation in a Kaehlerian manifold.
On the integration theorem for Lie groupoids
On the intersection forms of spin 4-manifolds bounded by spherical 3-manifolds.
On the invariant method in differential geometry of submanifolds
On the invariant variational sequences in mechanics
Summary: The -th order variational sequence is the quotient sequence of the De Rham sequence on the th jet prolongation of a fibered manifold, factored through its contact subsequence.In this paper, the first order variational sequence on a fibered manifold with one-dimensional base is considered. A new representation of all quotient spaces as some spaces of (global) forms is given. The factorization procedure is based on a modification of the interior Euler operator, used in the theory of (infinite)...
On the inverse problem of the calculus of variations for ordinary differential equations
Lepagean 2-form as a globally defined, closed counterpart of higher-order variational equations on fibered manifolds over one-dimensional bases is introduced, and elementary proofs of the basic theorems concerning the inverse problem of the calculus of variations, based on the notion of Lepagean 2-form and its properties, are given.
On the inverse variational problem in nonholonomic mechanics
The inverse problem of the calculus of variations in a nonholonomic setting is studied. The concept of constraint variationality is introduced on the basis of a recently discovered nonholonomic variational principle. Variational properties of first order mechanical systems with general nonholonomic constraints are studied. It is shown that constraint variationality is equivalent with the existence of a closed representative in the class of 2-forms determining the nonholonomic system. Together with...
On the inversion of pseudo-differential operators
On the Isotropy of Compact Minimal Surfaces in CPn.
On the iterated absolute differentiation on some functional bundles
We deduce further properties of connections on the functional bundle of all smooth maps between the fibers over the same base point of two fibered manifolds over the same base, which we introduced in [2]. In particular, we define the vertical prolongation of such a connection, discuss the iterated absolute differentiation by means of an auxiliary linear connection on the base manifold and prove the general Ricci identity.
On the Jäger-Kaul theorem concerning harmonic maps
On the jets of fibred manifold morphisms
On the jets of foliation respecting maps
Using Weil algebra techniques, we determine all finite dimensional homomorphic images of germs of foliation respecting maps.
On the Kähler geometry of the Hilbert-Schmidt Grassmannian.
On the Kobayashi metric for perturbations of the ball.