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Laplace-Beltrami Operator of a Helicoidal Hypersurface in Four-Space
, 2016 We introduce helicoidal hypersurface in the four dimensional Euclidean space. We calculate the mean and the Gaussian curvature, and some relations of the helicoidal hypersurface.
Erhan Güler, M. Magid, Y. Yaylı
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Modeling and Tracking of Maneuvering Extended Object With Random Hypersurface
IEEE Sensors Journal, 2021Extended object tracking, an important and emerging research field, has attracted attention for applications in civilian and military fields. However, the modeling and tracking of maneuvering extended objects still face challenges that need to be solved ...
Li-Fan Sun +4 more
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Hypersurfaces with Congruent Geodesics
Mathematische Nachrichten, 1992It is the purpose of this paper to prove the following theorem: Let \(M\) be a compact hypersurface of a complete, simply connected space \(N\) of constant curvature, and suppose that all geodesics of \(M\) are congruent in \(N\). Then \(M\) is an extrinsic sphere of positive curvature. The article contains many nice geometric ideas.
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The Convex Hull of a Hypersurface
Proceedings of the London Mathematical Society, 1985Given a codimension 1 smooth immersed submanifold \(M^ m\) in \(E^{m+1}\), the authors study the structure of the frontier H(f) of the convex hull of the image of \(M^ m\) in \(E^{m+1}\). First of all, they show that there exists a star-shaped smooth embedding h of the m-sphere \(S^ m\) into \(E^{m+1}\) with \(H(h)=H(f)\). Using this, a panel structure
Robertson, S. A., Romero-Fuster, M. C.
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On a Variational Problem on Hypersurfaces
Journal of the London Mathematical Society, 1973\«\dV £ cm, (1) M where cm denotes the area of a unit m-sphere. The equality sign of (1) holds when and only when M is a hypersphere in E. In order to know whether the inequality (1) can be improved for some given hypersurfaces in E, it is important to know the S-hypersurfaces in E, i.e., the stable hypersurfaces in E with respect to the integral ot ...
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