Eine differentialgeometrische Kennzeichnung der allgemeinen Dupinschen Zykliden.
Eine durch das Kleinsche Übertragungsprinzip vermittelte projektive Differentialgeometrie der windschiefen Flächen.
Exterior differential systems, Lie algebra cohomology, and the rigidity of homogenous varieties
These are expository notes from the 2008 Srní Winter School. They have two purposes: (1) to give a quick introduction to exterior differential systems (EDS), which is a collection of techniques for determining local existence to systems of partial differential equations, and (2) to give an exposition of recent work (joint with C. Robles) on the study of the Fubini-Griffiths-Harris rigidity of rational homogeneous varieties, which also involves an advance in the EDS technology.
Feuilletages conformes
Dans cet article nous montrons que tout feuilletage conforme, transversalement analytique, de codimension supérieure ou égale à trois sur une variété compacte connexe est transversalement Möbius ou riemannien. Ce théorème peut être vu comme une généralisation, transversalement à un feuilletage, du théorème Ferrand-Obata.
Formes différentielles sur l'espace projectif réel sous l'action du groupe linéaire général.
General-affine invariants of plane curves and space curves
We present a fundamental theory of curves in the affine plane and the affine space, equipped with the general-affine groups and , respectively. We define general-affine length parameter and curvatures and show how such invariants determine the curve up to general-affine motions. We then study the extremal problem of the general-affine length functional and derive a variational formula. We give several examples of curves and also discuss some relations with equiaffine treatment and projective...
Geometria proiettiva differenziale. I [Book]
Geometria proiettiva differenziale. II [Book]
Geometric interpretations of some Jordan algebras.
Grassmann manifold in the projective space with characteristics consisting of a quadric and two planes
Some results in the geometry of four-parametric manifolds of three-dimensional spaces in the projective space are found. The properties of such a manifold with characteristics consisting of a quadric and two planes are studied. The properties of the manifold dual to are found. Some results in the geometry of linear spaces from [1],[2],[3],[4] are used. The notation of the quantities is the same as in [4].
Introduction à la géométrie projective différentielle des surfaces [Book]
Invariant differential pairings.
Invariants and calculus for projective geometries.
Jednoparametrické systémy projektivních prostorů dimense v prostoru dimense
Kennzeichnung projektiver Abbildungsscharen, die mit Unterraumscharen des n-dimensionalen Raumes verknüpft sind.
Le direzioni caratteristiche di una trasformazione puntuale
Linien, Flächen und höhere Gebilde in mehrfach ausgedehnten Gausschen und Riemannschen Räumen
Neifeld’s Connection Inducedon the Grassmann Manifold
The work concerns to investigations in the field of differential geometry. It is realized by a method of continuations and scopes of G. F. Laptev which generalizes a moving frame method and Cartan’s exterior forms method and depends on calculation of exterior differential forms. The Grassmann manifold (space of all -planes) is considered in the -dimensional projective space . Principal fiber bundle of tangent linear frames is arised above this manifold. Typical fiber of the principal fiber bundle...
Nombre de rotation, structures géométriques sur un cercle et groupe de Bott-Virasoro
Une classification complète des stabilisateurs coadjoints du groupe de Bott-Virasoro est obtenue par une méthode essentiellement géométrique. L’outil de base est le nombre de rotation d’un difféomorphisme du cercle. En particulier, nous mettons en évidence la présence de groupes d’isotropie non-connexes et montrons que la transformation de Miura des opérateurs de Hill peut s’interpréter comme une application moment sur l’espace des structures affines du cercle.
Note on the Theory of -Pair of Manifolds in the Projective space