27 citations · 149 across the 22 of their papers we have counts for
23 papers
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…
Palatini Variation in Generalized Geometry and String Effective Actions
Branislav Jurco, Filip Moucka, Jan Vysoky
We develop the Palatini formalism within the framework of generalized Riemannian geometry of Courant algebroids. In this context, the Palatini variation of a generalized Einstein-H…
Graded Generalized Geometry
Jan Vysoky
Generalized geometry finds many applications in the mathematical description of some aspects of string theory. In a nutshell, it explores various structures on a generalized tangen…
Global Theory of Graded Manifolds
Jan Vysoky
A theory of graded manifolds can be viewed as a generalization of differential geometry of smooth manifolds. It allows one to work with functions which locally depend not only on o…
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…
Effective Actions for -Models of Poisson-Lie Type
Branislav Jurco, Jan Vysoky
(Quasi-)Poisson-Lie T-duality of string effective actions is described in the framework of generalized geometry of Courant algebroids. The approach is based on a generalization of…
Poisson-Lie T-duality of String Effective Actions: A New Approach to the Dilaton Puzzle
Branislav Jurco, Jan Vysoky
For a particular class of backgrounds, equations of motion for string sigma models targeted in mutually dual Poisson-Lie groups are equivalent. This phenomenon is called the Poisso…
Kaluza-Klein Reduction of Low-Energy Effective Actions: Geometrical Approach
Jan Vysoky
Equations of motion of low-energy string effective actions can be conveniently described in terms of generalized geometry and Levi-Civita connections on Courant algebroids. This ap…
Courant Algebroid Connections and String Effective Actions
Branislav Jurco, Jan Vysoky
Courant algebroids are a natural generalization of quadratic Lie algebras, appearing in various contexts in mathematical physics. A connection on a Courant algebroid gives an analo…
Geometry of Membrane Sigma Models
Jan Vysoky
String theory still remains one of the promising candidates for a unification of the theory of gravity and quantum field theory. One of its essential parts is relativistic descript…
Generalized geometry and non-symmetric gravity
Branislav Jurco, Fech Scen Khoo, Peter Schupp +1
Generalized geometry provides the framework for a systematic approach to non-symmetric metric gravity theory and naturally leads to an Einstein-Kalb-Ramond gravity theory with tota…
Heterotic Reduction of Courant Algebroid Connections and Einstein-Hilbert Actions
Branislav Jurco, Jan Vysoky
We discuss Levi-Civita connections on Courant algebroids. We define an appropriate generalization of the curvature tensor and compute the corresponding scalar curvatures in the exa…
Leibniz algebroids, generalized Bismut connections and Einstein-Hilbert actions
Branislav Jurco, Jan Vysoky
Connection, torsion and curvature are introduced for general (local) Leibniz algebroids. Generalized Bismut connection on is an example leading to a sca…
Extended generalized geometry and a DBI-type effective action for branes ending on branes
Branislav Jurco, Peter Schupp, Jan Vysoky
Starting from the usual bosonic membrane action, we develop the geometry suitable for the description of -brane backgrounds. Using the tools of generalized geometry we derive th…
Nambu-Poisson Gauge Theory
Branislav Jurco, Peter Schupp, Jan Vysoky
We generalize noncommutative gauge theory using Nambu-Poisson structures to obtain a new type of gauge theory with higher brackets and gauge fields. The approach is based on covari…
On the Generalized Geometry Origin of Noncommutative Gauge Theory
Branislav Jurco, Peter Schupp, Jan Vysoky
We discuss noncommutative gauge theory from the generalized geometry point of view. We argue that the equivalence between the commutative and semiclassically noncommutative DBI act…
Poisson-Lie Sigma Models on Drinfel'd double
Jan Vysoky, Ladislav Hlavaty
Poisson sigma models represent an interesting use of Poisson manifolds for the construction of a classical field theory. Their definition in the language of fibre bundles is shown…
p-Brane Actions and Higher Roytenberg Brackets
Branislav Jurco, Peter Schupp, Jan Vysoky
Motivated by the quest to understand the analog of non-geometric flux compactification in the context of M-theory, we study higher dimensional analogs of generalized Poisson sigma…
Manin supertriples and Drinfel'd superdoubles in low dimensions
Ladislav Hlavaty, Jan Vysoky
Defining the real Lie superalgebra as real --graded vector space we classify real Manin supertriples and Drinfel'd superdoubles of superdimensions (2,2), (4,2) and (2,4). They…