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Keywords = strictly convex plane curve

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18 pages, 338 KiB  
Article
Parallel Locally Strictly Convex Surfaces in Four-Dimensional Affine Space Contained in Hyperquadrics
by Paweł Witowicz
Symmetry 2021, 13(9), 1575; https://doi.org/10.3390/sym13091575 - 26 Aug 2021
Cited by 1 | Viewed by 1310
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Section Mathematics)
14 pages, 287 KiB  
Article
Area Properties of Strictly Convex Curves
by Dong-Soo Kim, Young Ho Kim and Yoon-Tae Jung
Mathematics 2019, 7(5), 391; https://doi.org/10.3390/math7050391 - 29 Apr 2019
Cited by 4 | Viewed by 2701
Abstract
We study functions defined in the plane E 2 in which level curves are strictly convex, and investigate area properties of regions cut off by chords on the level curves. In this paper we give a partial answer to the question: Which function [...] Read more.
We study functions defined in the plane E 2 in which level curves are strictly convex, and investigate area properties of regions cut off by chords on the level curves. In this paper we give a partial answer to the question: Which function has level curves whose tangent lines cut off from a level curve segment of constant area? In the results, we give some characterization theorems regarding conic sections. Full article
(This article belongs to the Section E1: Mathematics and Computer Science)
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