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Gamma-function and Gaussian-sum-function

Helversen-Pasotto, A. (1993)

Proceedings of the Winter School "Geometry and Physics"

After some remarks about the analogy between the classical gamma-function and Gaussian sums over finite fields a complete, very short explicit proof is given of an identity expressing a certain sum of products of Gaussian sums as a product of Gaussian sums. This identity is an analogue of the classical Barnes’ first lemma for the gamma-function. Four multiplicative characters of a finite field are concerned; the usually necessary restrictions on the triviality of certain products of these characters...

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...

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 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.

Generalized Einstein manifolds

Formella, Stanisław (1990)

Proceedings of the Winter School "Geometry and Physics"

[For the entire collection see Zbl 0699.00032.] A manifold (M,g) is said to be generalized Einstein manifold if the following condition is satisfied ( ∇ X S ) ( Y , Z ) = σ ( X ) g ( Y , Z ) + ν ( Y ) g ( X , Z ) + ν ( Z ) g ( X , Y ) where S(X,Y) is the Ricci tensor of (M,g) and σ (X), ν (X) are certain ℓ -forms. In the present paper the author studies properties of conformal and geodesic mappings of generalized Einstein manifolds. He gives the local classification of generalized Einstein manifolds when g( ψ (X), ψ (X)) ≠ 0 .

Generalized Jacobi morphisms in variational sequences

Francaviglia, Mauro, Palese, Marcella (2002)

Proceedings of the 21st Winter School "Geometry and Physics"

Summary: We provide a geometric interpretation of generalized Jacobi morphisms in the framework of finite order variational sequences. Jacobi morphisms arise classically as an outcome of an invariant decomposition of the second variation of a Lagrangian. Here they are characterized in the context of generalized Lagrangian symmetries in terms of variational Lie derivatives of generalized Euler-Lagrange morphisms. We introduce the variational vertical derivative and stress its link with the classical...

Generalized shape theory

Deleanu, Aristide, Hilton, Peter (1977)

General topology and its relations to modern analysis and algebra IV

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