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In this paper we solve the problem of finding integrals of equations determining the Killing tensors on an $n$ -dimensional differentiable manifold $M$ endowed with an equiaffine $S L (n,)$ -structure and discuss possible applications of obtained results in Riemannian geometry.

The Monge-Ampère equation and affine maximal surfaces.

Kozlowski, Michael (1993)

Publications de l'Institut Mathématique. Nouvelle Série

The osculating hyperquadrics of the three-component distribution in affine space

Marina F. Grebenyuk (2001)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Thomsen Surfaces in Affine 4-Space.

Luc Vrancken (1996)

Monatshefte für Mathematik

Torsion Free Connections, Topology, Geometry and Differential Operators on Smooth Manifolds

Neda Bokan (2000)

Zbornik Radova

Traceless cubic forms on statistical manifolds and Tchebychev geometry

Hiroshi Matsuzoe (2005)

Banach Center Publications

Geometry of traceless cubic forms is studied. It is shown that the traceless part of the cubic form on a statistical manifold determines a conformal-projective equivalence class of statistical manifolds. This conformal-projective equivalence on statistical manifolds is a natural generalization of conformal equivalence on Riemannian manifolds. As an application, Tchebychev type immersions in centroaffine immersions of codimension two are studied.

Translation foliations of codimension one on compact affine manifolds

Francisco Turiel (1997)

Banach Center Publications

Consider two foliations $ℱ_{1}$ and $ℱ_{2}$ , of dimension one and codimension one respectively, on a compact connected affine manifold $(M, \nabla)$ . Suppose that $\nabla_{T ℱ_{1}} T ℱ_{2} \subset T ℱ_{2}$ ; $\nabla_{T ℱ_{2}} T ℱ_{1} \subset T ℱ_{1}$ and $T M = T ℱ_{1} \oplus T ℱ_{2}$ . In this paper we show that either $ℱ_{2}$ is given by a fibration over $S^{1}$ , and then $ℱ_{1}$ has a great degree of freedom, or the trace of $ℱ_{1}$ is given by a few number of types of curves which are completely described. Moreover we prove that $ℱ_{2}$ has a transverse affine structure.

Two-parametric systems of three-dimensional spaces in a unimodular six-dimensional affine space

Josef Srovnal (1986)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Über die isotropoen Gegenstücke der Minimalfläche von Scherk.

Karl Strubecker (1977)

Journal für die reine und angewandte Mathematik

Über geschlossene affine Zwangläufe in der Ebene.

Christoph Lübbert (1977)

Manuscripta mathematica

Un survol de la théorie des variétés affines

Yves Carrière (1987/1988)

Séminaire de théorie spectrale et géométrie

Une correspondance par parallélisme partiel entre deux variétés réglées de l’espace $S_{5}$

Stefania Ruscior (1970)

Archivum Mathematicum

Variational problems and PDEs in affine differential geometry

H. Z. Li (2005)

Banach Center Publications

This paper is part of the autumn school on "Variational problems and higher order PDEs for affine hypersurfaces". We discuss variational problems in equiaffine differential geometry, centroaffine differential geometry and relative differential geometry, which have been studied by Blaschke [Bla], Chern [Ch], C. P. Wang [W], Li-Li-Simon [LLS], and Calabi [Ca-II]. We first derive the Euler-Lagrange equations in these settings; these equations are complicated, strongly nonlinear fourth order PDEs. We...

Zur Affinoberfläche konvexer Körper.

Kurt Leichtweiß (1986)

Manuscripta mathematica

Zur äquiformen Geometrie in der Ebene

Zdeněk Jankovský, Miroslav Šejdl (1987)

Aplikace matematiky

Im Artikel werden die Integral- und Differentialgrundinvarianten (Bogen, Krümmung) der ebenen Kurve angesichts der äquiformen Gruppe ( $ℰ$ -Gruppe) bei der Anwendung der komplexen Symbolik hergeleitet. Weiter werden die $ℰ$ -minimalen Kurven, $ℰ$ -Geraden und $ℰ$ -Kreise von der $ℰ$ -Geometrie festgestellt; im euklidischen Modell handelt es sich um die Geraden, Kreise und logarithmischen Spiralen.

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