The Frobenius Theorem for Graded Manifolds and Applications in Graded Symplectic Geometry
نویسندگان
چکیده
The Frobenius theorem is extended from supermanifolds to N-graded manifolds. It is shown, both for super and N-graded manifolds, that the characteristic distribution of a presymplectic submanifold is involutive and hence integrable.
منابع مشابه
Graded Differential Geometry of Graded Matrix Algebras
We study the graded derivation-based noncommutative differential geometry of the Z2-graded algebra M(n|m) of complex (n+m)× (n+m)-matrices with the “usual block matrix grading” (for n 6= m). Beside the (infinite-dimensional) algebra of graded forms the graded Cartan calculus, graded symplectic structure, graded vector bundles, graded connections and curvature are introduced and investigated. In...
متن کاملBUCKLING ANALYSIS OF FUNCTIONALLY GRADED MINDLIN PLATES SUBJECTED TO LINEARLY VARYING IN-PLANE LOADING USING POWER SERIES METHOD OF FROBENIUS
In this paper, buckling behavior of moderately thick functionally graded rectangular plates resting on elastic foundation subjected to linearly varying in-plane loading is investigated. The neutral surface position for a functionally graded plate which its material properties vary in the thickness direction is determined. Based on the first-order shear deformation plate theory and the neutral s...
متن کاملESI The Erwin Schr
We study the graded derivation-based noncommutative diierential geometry of the Z 2-graded algebra M (njm) of complex (n + m) (n + m)-matrices with the \usual block matrix grading" (for n 6 = m). Beside the (innnite-dimensional) algebra of graded forms the graded Cartan calculus, graded symplectic structure, graded vector bundles, graded connections and curvature are introduced and investigated...
متن کاملLoop Space and Deformations of De Rham Cohomology
We show that the deformations of the de Rham cohomology of a closed simply connected KK ahler manifold are governed by the dual of real-valued cohomology of its free loop space. A currently very active eld in Mathematics is the theory of quantum cohomol-ogy, which provides a special kind of deformations of the multiplication structure on the de Rham cohomology of symplectic manifolds. The mathe...
متن کاملLagrangian Embeddings, Maslov Indexes and Integer Graded Symplectic Floer Cohomology
We define an integer graded symplectic Floer cohomology and a spectral sequence which are new invariants for monotone Lagrangian sub-manifolds and exact isotopies. Such an integer graded Floer cohomology is an integral lifting of the usual Floer-Oh cohomology with ZΣ(L) grading. As one of applications of the spectral sequence, we offer an affirmative answer to an Audin’s question for oriented, ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009