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Gauge-natural field theories and Noether theorems: canonical covariant conserved currents

Palese, Marcella, Winterroth, Ekkehart (2006)

Proceedings of the 25th Winter School "Geometry and Physics"

Summary: We specialize in a new way the second Noether theorem for gauge-natural field theories by relating it to the Jacobi morphism and show that it plays a fundamental role in the derivation of canonical covariant conserved quantities. In particular we show that Bergmann-Bianchi identities for such theories hold true covariantly and canonically only along solutions of generalized gauge-natural Jacobi equations. Vice versa, all vertical parts of gauge-natural lifts of infinitesimal principal automorphisms...

Gaussian curvature based tangential redistribution of points on evolving surfaces

Medľa, Matej, Mikula, Karol (2017)

Proceedings of Equadiff 14

There exist two main methods for computing a surface evolution, level-set method and Lagrangian method. Redistribution of points is a crucial element in a Lagrangian approach. In this paper we present a point redistribution that compress quads in the areas with a high Gaussian curvature. Numerical method is presented for a mean curvature flow of a surface approximated by quads.

General construction of Banach-Grassmann algebras

Vladimir G. Pestov (1992)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We show that a free graded commutative Banach algebra over a (purely odd) Banach space E is a Banach-Grassmann algebra in the sense of Jadczyk and Pilch if and only if E is infinite-dimensional. Thus, a large amount of new examples of separable Banach-Grassmann algebras arise in addition to the only one example previously known due to A. Rogers.

General Nijenhuis tensor: an example of a secondary invariant

Studený, Václav (1996)

Proceedings of the Winter School "Geometry and Physics"

The author considers the Nijenhuis map assigning to two type (1,1) tensor fields α , β a mapping 〈 α , β 〉 : ( ξ , ζ ) ↦ [ α ( ξ ) , β ( ζ ) ] + α ∘ β ( [ ξ , ζ ] ) - α ( [ ξ , β ( ζ ) ] ) - β ( [ α ( ξ ) , ζ ) ] ) , where ξ , ζ are vector fields. Then 〈 α , β 〉 is a type (2,1) tensor field (Nijenhuis tensor) if and only if [ α , β ] = 0 . Considering a smooth manifold X with a smooth action of a Lie group, a secondary invariant may be defined as a mapping whose area of invariance is restricted to the inverse image of an invariant subset of X under another invariant mapping. The author recognizes a secondary invariant related to the...

General spectral flow formula for fixed maximal domain

Bernhelm Booss-Bavnbek, Chaofeng Zhu (2005)

Open Mathematics

We consider a continuous curve of linear elliptic formally self-adjoint differential operators of first order with smooth coefficients over a compact Riemannian manifold with boundary together with a continuous curve of global elliptic boundary value problems. We express the spectral flow of the resulting continuous family of (unbounded) self-adjoint Fredholm operators in terms of the Maslov index of two related curves of Lagrangian spaces. One curve is given by the varying domains, the other by...

General structured bundles

Cabras, Antonella, Kolář, Ivan, Modugno, Marco (1991)

Proceedings of the Winter School "Geometry and Physics"

Summary: [For the entire collection see Zbl 0742.00067.]A general theory of fibre bundles structured by an arbitrary differential-geometric category is presented. It is proved that the structured bundles of finite type coincide with the classical associated bundles.

General theory of Lie derivatives for Lorentz tensors

Lorenzo Fatibene, Mauro Francaviglia (2011)

Communications in Mathematics

We show how the ad hoc prescriptions appearing in 2001 for the Lie derivative of Lorentz tensors are a direct consequence of the Kosmann lift defined earlier, in a much more general setting encompassing older results of Y. Kosmann about Lie derivatives of spinors.

General-affine invariants of plane curves and space curves

Shimpei Kobayashi, Takeshi Sasaki (2020)

Czechoslovak Mathematical Journal

We present a fundamental theory of curves in the affine plane and the affine space, equipped with the general-affine groups GA ( 2 ) = GL ( 2 , ℝ ) ⋉ ℝ 2 and GA ( 3 ) = GL ( 3 , ℝ ) ⋉ ℝ 3 , respectively. We define general-affine length parameter and curvatures and show how such invariants determine the curve up to general-affine motions. We then study the extremal problem of the general-affine length functional and derive a variational formula. We give several examples of curves and also discuss some relations with equiaffine treatment and projective...

Generalization of p-regularity notion and tangent cone description in the singular case

Wiesław Grzegorczyk, Beata Medak, Alexey A. Tret’yakov (2012)

Annales UMCS, Mathematica

The theory of p-regularity has approximately twenty-five years’ history and many results have been obtained up to now. The main result of this theory is description of tangent cone to zero set in singular case. However there are numerous nonlinear objects for which the p-regularity condition fails, especially for p > 2. In this paper we generalize the p-regularity notion as a starting point for more detailed consideration based on different p-factor operators constructions.

Generalizations of Melin's inequality to systems

Raymond Brummelhuis (2001)

Journées équations aux dérivées partielles

We discuss a recent necessary and sufficient condition for Melin's inequality for a class of systems of pseudodifferential operators.

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