Parallel Locally Strictly Convex Surfaces in Four-Dimensional Affine Space Contained in Hyperquadrics

Parallel Locally Strictly Convex Surfaces in Four-Dimensional Affine Space Contained in Hyperquadrics

Locally strictly convex surfaces in four-dimensional affine space are studied from a perspective of the affine structure invented by Nuño-Ballesteros and Sánchez, which is especially suitable in convex geometry. The surfaces that are embedded in locally strictly convex hyperquadrics are classified u...

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Bibliographic Details
Main Author: Paweł Witowicz
Format: Article
Language:English
Published: MDPI AG 2021-08-01
Series:Symmetry
Subjects:
affine metric
strictly convex surface
symmetric equiaffine transversal bundle
antisymmetric equiaffine transversal bundle
hyperquadric
Online Access:https://www.mdpi.com/2073-8994/13/9/1575
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spelling doaj-1692588990394d93bea9e592a9c1dfb82021-09-26T01:30:43ZengMDPI AGSymmetry2073-89942021-08-01131575157510.3390/sym13091575Parallel Locally Strictly Convex Surfaces in Four-Dimensional Affine Space Contained in HyperquadricsPaweł Witowicz0The Faculty of Mathematics and Applied Physics, Rzeszów University of Technology, al. Powstańcow Warszawy 12, 35-959 Rzeszów, PolandLocally strictly convex surfaces in four-dimensional affine space are studied from a perspective of the affine structure invented by Nuño-Ballesteros and Sánchez, which is especially suitable in convex geometry. The surfaces that are embedded in locally strictly convex hyperquadrics are classified under assumptions that the second fundamental form is parallel with respect to the induced connection and the normal connection is compatible with a metric on the transversal bundle. Both connections are induced by a canonical transversal plane bundle, which is defined by certain symmetry conditions. The obtained surfaces are always products of an ellipse and a conical planar curve.https://www.mdpi.com/2073-8994/13/9/1575affine metricstrictly convex surfacesymmetric equiaffine transversal bundleantisymmetric equiaffine transversal bundlehyperquadric
collection DOAJ
language English
format Article
sources DOAJ
author Paweł Witowicz
spellingShingle Paweł Witowicz
Parallel Locally Strictly Convex Surfaces in Four-Dimensional Affine Space Contained in Hyperquadrics
Symmetry
affine metric
strictly convex surface
symmetric equiaffine transversal bundle
antisymmetric equiaffine transversal bundle
hyperquadric
author_facet Paweł Witowicz
author_sort Paweł Witowicz
title Parallel Locally Strictly Convex Surfaces in Four-Dimensional Affine Space Contained in Hyperquadrics
title_short Parallel Locally Strictly Convex Surfaces in Four-Dimensional Affine Space Contained in Hyperquadrics
title_full Parallel Locally Strictly Convex Surfaces in Four-Dimensional Affine Space Contained in Hyperquadrics
title_fullStr Parallel Locally Strictly Convex Surfaces in Four-Dimensional Affine Space Contained in Hyperquadrics
title_full_unstemmed Parallel Locally Strictly Convex Surfaces in Four-Dimensional Affine Space Contained in Hyperquadrics
title_sort parallel locally strictly convex surfaces in four-dimensional affine space contained in hyperquadrics
publisher MDPI AG
series Symmetry
issn 2073-8994
publishDate 2021-08-01
description Locally strictly convex surfaces in four-dimensional affine space are studied from a perspective of the affine structure invented by Nuño-Ballesteros and Sánchez, which is especially suitable in convex geometry. The surfaces that are embedded in locally strictly convex hyperquadrics are classified under assumptions that the second fundamental form is parallel with respect to the induced connection and the normal connection is compatible with a metric on the transversal bundle. Both connections are induced by a canonical transversal plane bundle, which is defined by certain symmetry conditions. The obtained surfaces are always products of an ellipse and a conical planar curve.
topic affine metric
strictly convex surface
symmetric equiaffine transversal bundle
antisymmetric equiaffine transversal bundle
hyperquadric
url https://www.mdpi.com/2073-8994/13/9/1575
work_keys_str_mv AT pawełwitowicz parallellocallystrictlyconvexsurfacesinfourdimensionalaffinespacecontainedinhyperquadrics
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