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A five-dimensional classical framework for gravitational and quantum phenomena. [PDF]
Sci RepStrubbe F.
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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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Concurrent Vector Fields on Lightlike Hypersurfaces
Mathematics, 2021Mehmet Gulbahar, Erol Kılıç
exaly
Isoparametric hypersurfaces with four principal curvatures, IV
Journal of Differential Geometry, 2020Quo-Shin Chi
exaly