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Diffeomorphisms conformal on distributions

Kamil Niedziałomski (2009)

Annales Polonici Mathematici

Let f:M → N be a local diffeomorphism between Riemannian manifolds. We define the eigenvalues of f to be the eigenvalues of the self-adjoint, positive definite operator df*df:TM → TM, where df* denotes the operator adjoint to df. We show that if f is conformal on a distribution D, then d i m V λ 2 d i m D - d i m M , where V λ denotes the eigenspace corresponding to the coefficient of conformality λ of f. Moreover, if f has distinct eigenvalues, then there is locally a distribution D such that f is conformal on D if and only...

Diffeomorphisms constructively associated with mutually diverging spacetimes which allow a natural identification of event points in general relativity. Part I

Gaetano Zampieri (1982)

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

In questo lavoro si dà una definizione di divergenza fra cronotopi della Relatività Generale e si costruisce un criterio per l'identificazione dei punti eventi di cronotopi divergenti che appartengono ad una classe consistente con la presenza di campi elettromagnetici nel vuoto.

Diffeomorphisms constructively associated with mutually diverging spacetimes which allow a natural identification of event points in general relativity. Part II

Gaetano Zampieri (1982)

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

In questo lavoro si dà una definizione di divergenza fra cronotopi della Relatività Generale e si costruisce un criterio per l'identificazione dei punti eventi di cronotopi divergenti che appartengono ad una classe consistente con la presenza di campi elettromagnetici nel vuoto.

Differentiability and Approximate Differentiability for Intrinsic Lipschitz Functions in Carnot Groups and a Rademacher Theorem

Bruno Franchi, Marco Marchi, Raul Paolo Serapioni (2014)

Analysis and Geometry in Metric Spaces

A Carnot group G is a connected, simply connected, nilpotent Lie group with stratified Lie algebra. We study intrinsic Lipschitz graphs and intrinsic differentiable graphs within Carnot groups. Both seem to be the natural analogues inside Carnot groups of the corresponding Euclidean notions. Here ‘natural’ is meant to stress that the intrinsic notions depend only on the structure of the algebra of G. We prove that one codimensional intrinsic Lipschitz graphs are sets with locally finite G-perimeter....

Differential Batalin-Vilkovisky algebras arising from twilled Lie-Rinehart algebras

Johannes Huebschmann (2000)

Banach Center Publications

Twilled L(ie-)R(inehart)-algebras generalize, in the Lie-Rinehart context, complex structures on smooth manifolds. An almost complex manifold determines an "almost twilled pre-LR algebra", which is a true twilled LR-algebra iff the almost complex structure is integrable. We characterize twilled LR structures in terms of certain associated differential (bi)graded Lie and G(erstenhaber)-algebras; in particular the G-algebra arising from an almost complex structure is a (strict) d(ifferential) G-algebra...

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