Open Access
November 2012 Some New Characteristic Properties of the A-Pedal Hypersurfaces in $E^{n+1}$
Ayhan Sarioğlugil, Sidika Tül, Nuri Kuruoğlu
Missouri J. Math. Sci. 24(2): 156-166 (November 2012). DOI: 10.35834/mjms/1352138561


The primary purpose of this paper is to present the definition of the a-pedal hypersurface with respect to a point in the interior of a closed, convex and smooth hypersurface $M$. The secondary purpose of this paper is to give some new characteristic properties of the a-pedal hypersurfaces related to the support function, Gauss curvature, mean curvature, the first and second fundamental forms and their coefficients of $M$ (Section 3). Using the classical methods of the hypersurfaces in differential geometry we have established that the support function $h_{a}$ of the a-pedal hypersurface $M_{a}$ is equal to $\frac{h^{a+1}}{P_{a}}$ where $P_{a}^{2}=h^{2}+a^{2}\overset{III}{\nabla }(h,h)$.


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Ayhan Sarioğlugil. Sidika Tül. Nuri Kuruoğlu. "Some New Characteristic Properties of the A-Pedal Hypersurfaces in $E^{n+1}$." Missouri J. Math. Sci. 24 (2) 156 - 166, November 2012.


Published: November 2012
First available in Project Euclid: 5 November 2012

zbMATH: 1258.53010
MathSciNet: MR3052413
Digital Object Identifier: 10.35834/mjms/1352138561

Primary: 53A05
Secondary: 53A07 , 53A15 , 53C45

Rights: Copyright © 2012 Central Missouri State University, Department of Mathematics and Computer Science

Vol.24 • No. 2 • November 2012
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