Graded manifolds and pairs

2006 ◽  
pp. 65-72 ◽  
Author(s):  
Marjorie Batchelor
Keyword(s):  
Graded Manifolds

scholarly journals Higher Dimensional Holonomy Map for Rules Submanifolds in Graded Manifolds

2020 ◽  
Vol 8 (1) ◽  
pp. 68-91
Author(s):  
Gianmarco Giovannardi
Keyword(s):  
Characteristic Direction ◽  
Fixed Degree ◽  
One Dimensional ◽  
First Order ◽  
Natural Choice ◽  
Higher Dimensional ◽  
Graded Manifold ◽  
The One ◽  
Graded Manifolds ◽  
Holonomy Map

AbstractThe deformability condition for submanifolds of fixed degree immersed in a graded manifold can be expressed as a system of first order PDEs. In the particular but important case of ruled submanifolds, we introduce a natural choice of coordinates, which allows to deeply simplify the formal expression of the system, and to reduce it to a system of ODEs along a characteristic direction. We introduce a notion of higher dimensional holonomy map in analogy with the one-dimensional case [29], and we provide a characterization for singularities as well as a deformability criterion.

Submanifolds of Fixed Degree in Graded Manifolds for Perceptual Completion

2021 ◽  
pp. 47-55
Author(s):  
Giovanna Citti ◽  
Gianmarco Giovannardi ◽  
Manuel Ritoré ◽  
Alessandro Sarti
Keyword(s):  
Fixed Degree ◽  
Perceptual Completion ◽  
Graded Manifolds

scholarly journals Connections adapted to non-negatively graded structures

2019 ◽  
Vol 16 (02) ◽  
pp. 1950021
Author(s):  
Andrew James Bruce
Keyword(s):  
Vector Bundle ◽  
Geometric Structure ◽  
Vector Bundles ◽  
Natural Generalization ◽  
Lie Algebroids ◽  
Linear Formula ◽  
Natural Sense ◽  
Graded Structures ◽  
Graded Manifolds ◽  
Double Vector Bundle

Graded bundles are a particularly nice class of graded manifolds and represent a natural generalization of vector bundles. By exploiting the formalism of supermanifolds to describe Lie algebroids, we define the notion of a weighted[Formula: see text]-connection on a graded bundle. In a natural sense weighted [Formula: see text]-connections are adapted to the basic geometric structure of a graded bundle in the same way as linear [Formula: see text]-connections are adapted to the structure of a vector bundle. This notion generalizes directly to multi-graded bundles and in particular we present the notion of a bi-weighted[Formula: see text]-connection on a double vector bundle. We prove the existence of such adapted connections and use them to define (quasi-)actions of Lie algebroids on graded bundles.

scholarly journals Duality for Graded Manifolds

2017 ◽  
Vol 80 (1) ◽  
pp. 115-142 ◽  
Author(s):  
Janusz Grabowski ◽  
Michał Jóźwikowski ◽  
Mikołaj Rotkiewicz
Keyword(s):  
Graded Manifolds

scholarly journals CLASSICAL FIELD THEORY: ADVANCED MATHEMATICAL FORMULATION

2008 ◽  
Vol 05 (07) ◽  
pp. 1163-1189 ◽  
Author(s):  
G. SARDANASHVILY
Keyword(s):  
Field Theory ◽  
Mathematical Formulation ◽  
Classical Field Theory ◽  
Classical Field ◽  
Fibre Bundles ◽  
Graded Manifolds

In contrast with QFT, classical field theory can be formulated in strict mathematical terms of fibre bundles, graded manifolds and jet manifolds. Second Noether theorems provide BRST extension of this classical field theory by means of ghosts and antifields for the purpose of its quantization.

scholarly journals Weyl quantization of degree 2 symplectic graded manifolds

2021 ◽  
Author(s):  
Melchior Grützmann ◽  
Jean-Philippe Michel ◽  
Ping Xu
Keyword(s):  
Weyl Quantization ◽  
Graded Manifolds

An independence theorem for Lagrangian systems on graded manifolds

1984 ◽  
Vol 8 (2) ◽  
pp. 105-109 ◽  
Author(s):  
Andrea Barducci ◽  
Riccardo Giachetti ◽  
Emanuele Sorace
Keyword(s):  
Lagrangian Systems ◽  
Independence Theorem ◽  
Graded Manifolds
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