12 citations · 13 across the 6 of their papers we have counts for
7 papers · 1 filter
On the Integrability of Distributions in -graded Geometry
Rudolf Šmolka, Jan Vysoký
Integrability of distributions on -graded manifolds is examined. First, the Local Frobenius theorem -- the local existence of flat coordinates for an involutive distrib…
Flows on Graded Manifolds
Rudolf Smolka, Jan Vysoky
Flows of vector fields are an essential tool in differential geometry, with countless applications in both theory and practice. While they have been extensively studied for ordinar…
Three Examples of Graded Lie Groups
Jan Vysoky
Lie theory is, beyond any doubt, an absolutely essential part of differential geometry. It is therefore necessary to seek its generalization to -graded geometry. In par…
Threefold Nature of Graded Vector Bundles
Rudolf Smolka, Jan Vysoky
Graded vector bundles over a given -graded manifold can be defined in three different ways: certain sheaves of graded modules over the structure sheaf of the base grade…
Graded Jet Geometry
Jan Vysoky
Jet manifolds and vector bundles allow one to employ tools of differential geometry to study differential equations, for example those arising as equations of motions in physics. T…
Hitchhiker's Guide to Courant Algebroid Relations
Jan Vysoky
Courant algebroids provide a useful mathematical tool (not only) in string theory. It is thus important to define and examine their morphisms. To some extent, this was done before…