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Prescribing a fourth order conformal invariant on the standard sphere, part II : blow up analysis and applications

Zindine Djadli, Andrea Malchiodi, Mohameden Ould Ahmedou (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

In this paper we perform a fine blow up analysis for a fourth order elliptic equation involving critical Sobolev exponent, related to the prescription of some conformal invariant on the standard sphere ( 𝕊 n , h ) . We derive from this analysis some a priori estimates in dimension 5 and 6 . On 𝕊 5 these a priori estimates, combined with the perturbation result in the first part of the present work, allow us to obtain some existence result using a continuity method. On 𝕊 6 we prove the existence of at least one...

Principal prolongations and geometries modeled on homogeneous spaces

Jan Slovák (1996)

Archivum Mathematicum

We discuss frame bundles and canonical forms for geometries modeled on homogeneous spaces. Our aim is to introduce a geometric picture based on the non-holonomic jet bundles and principal prolongations as introduced in [Kolář, 71]. The paper has a partly expository character and we focus on very general aspects only. In the final section, various links to known results on the parabolic geometries are given briefly and some directions for further investigations are roughly indicated.

Projective plane motions with infinitely many straight trajectories

Adolf Karger (1985)

Aplikace matematiky

The paper deals with one-parametric projective plane motins with the property that all points of the inflexion cubic have straight trajectories. It is shown that such motions have in the general case projective equivalent trajectories and that the inflexion cubic is in general irreducible. The cases of the above mentioned motions with reducible inflexion cubic are discussed in detail. The connection with the Darboux property is also mentioned.

Projective relatedness and conformal flatness

Graham Hall (2012)

Open Mathematics

This paper discusses the connection between projective relatedness and conformal flatness for 4-dimensional manifolds admitting a metric of signature (+,+,+,+) or (+,+,+,−). It is shown that if one of the manifolds is conformally flat and not of the most general holonomy type for that signature then, in general, the connections of the manifolds involved are the same and the second manifold is also conformally flat. Counterexamples are provided which place limitations on the potential strengthening...

Projective spaces of second order.

Andrzej Miernowski, Witold Mozgawa (1997)

Collectanea Mathematica

Grassmannians of higher order appeared for the first time in a paper of A. Szybiak in the context of the Cartan method of moving frame. In the present paper we consider a special case of higher order Grassmannian, the projective space of second order. We introduce the projective group of second order acting on this space, derive its Maurer-Cartan equations and show that our generalized projective space is a homogeneous space of this group.

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