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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...

Distinguished geodesics and jacobi fields on first order jet spaces

Vladimir Balan, Nicoleta Voicu (2004)

Open Mathematics

In the framework of jet spaces endowed with a non-linear connection, the special curves of these spaces (h-paths, v-paths, stationary curves and geodesics) which extend the corresponding notions from Riemannian geometry are characterized. The main geometric objects and the paths are described and, in the case when the vertical metric is independent of fiber coordinates, the first two variations of energy and the extended Jacobi field equations are derived.

Distributions involutives singulières

Dominique Cerveau (1979)

Annales de l'institut Fourier

On étudie les distributions involutives, i.e. les modules D de champs de vecteurs stables par le crochet de Lie, au voisinage d’un point 0 singulier. Après s’être ramené au cas purement singulier, c’est-à-dire où tous les éléments de D s’annulent en 0, des hypothèses génériques portant sur la partie linéaire de D nous permettent d’obtenir la linéarisation.

Divergence operators and odd Poisson brackets

Yvette Kosmann-Schwarzbach, Juan Monterde (2002)

Annales de l’institut Fourier

We define the divergence operators on a graded algebra, and we show that, given an odd Poisson bracket on the algebra, the operator that maps an element to the divergence of the hamiltonian derivation that it defines is a generator of the bracket. This is the “odd laplacian”, Δ , of Batalin-Vilkovisky quantization. We then study the generators of odd Poisson brackets on supermanifolds, where divergences of graded vector fields can be defined either in terms of berezinian volumes or of graded connections. Examples...

Double linear connections

Alena Vanžurová (1991)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Double vector spaces

Alena Vanžurová (1987)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Duality of Hodge numbers of compact complex nilmanifolds

Takumi Yamada (2015)

Complex Manifolds

A compact K¨ahlerian manifoldM of dimension n satisfies hp,q(M) = hq,p(M) for each p, q.However, a compact complex manifold does not satisfy the equations in general. In this paper, we consider duality of Hodge numbers of compact complex nilmanifolds.

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