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F -manifolds and integrable systems of hydrodynamic type

Paolo Lorenzoni, Marco Pedroni, Andrea Raimondo (2011)

Archivum Mathematicum

We investigate the role of Hertling-Manin condition on the structure constants of an associative commutative algebra in the theory of integrable systems of hydrodynamic type. In such a framework we introduce the notion of F -manifold with compatible connection generalizing a structure introduced by Manin.

∇-flat functions on manifolds

Wojciech Kozłowski (2004)

Annales Polonici Mathematici

We investigate ∇-flat and pointwise-∇-flat functions on affine and Riemannian manifolds. We show that the set of all ∇-flat functions on (M,∇) is a ring which has interesting properties similar to the ring of polynomial functions.

Foliations of lightlike hypersurfaces and their physical interpretation

Krishan Duggal (2012)

Open Mathematics

This paper deals with a family of lightlike (null) hypersurfaces (H u) of a Lorentzian manifold M such that each null normal vector ℓ of H u is not entirely in H u, but, is defined in some open subset of M around H u. Although the family (H u) is not unique, we show, subject to some reasonable condition(s), that the involved induced objects are independent of the choice of (H u) once evaluated at u = constant. We use (n+1)-splitting Lorentzian manifold to obtain a normalization of ℓ and a well-defined...

Formes normales d’une métrique mixte analytique réelle générique

Tomasz Miernowski (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

Par une métrique mixte on comprend une métrique définie dans un domaine du plan, changeant de caractère – sur une région elle est riemannienne, sur une autre lorentzienne. On se place dans un point appartenant à la frontière entre ces deux régions et on cherche une forme locale « la plus simple » de notre métrique – un problème analogue à l’existance des coordonnées isothermes dans le cas classique, riemannien ou lorentzien. On montre que génériquement on peut se ramener à un seul modèle conforme...

From Euler-Lagrange equations to canonical nonlinear connections

Mircea Neagu (2006)

Archivum Mathematicum

The aim of this paper is to construct a canonical nonlinear connection Γ = ( M ( α ) β ( i ) , N ( α ) j ( i ) ) on the 1-jet space J 1 ( T , M ) from the Euler-Lagrange equations of the quadratic multi-time Lagrangian function L = h α β ( t ) g i j ( t , x ) x α i x β j + U ( i ) ( α ) ( t , x ) x α i + F ( t , x ) .

Currently displaying 321 – 340 of 1304