Lorentz hypersurfaces satisfying $$\triangle \vec {H}= \alpha \vec {H}$$ ▵ H → = α H → with non diagonal shape operator [PDF]
Sao Paulo Journal of Mathematical Sciences, 2016 We study Lorentz hypersurfaces $M_{1}^{n}$ in $E_{1}^{n+1}$ satisfying $\triangle \vec {H}= α\vec {H}$ with non diagonal shape operator, having complex eigenvalues. We prove that every such Lorentz hypersurface in $E_{1}^{n+1}$ having at most five distinct principal curvatures has constant mean curvature.
Andreas Arvanitoyeorgos +2 more
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Rigidity of diagonally embedded triangle groups [PDF]
Canadian Mathematical Bulletin, 2020 AbstractWe show local rigidity of hyperbolic triangle groups generated by reflections in pairs of n-dimensional subspaces of $\mathbb {R}^{2n}$ obtained by composition of the geometric representation in $\mathsf {PGL}(2,\mathbb {R})$ with the diagonal embeddings into $\mathsf {PGL}(2n,\mathbb {R})$ and $\mathsf {PSp}^\pm (2n,\mathbb {R})$ .
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Dijagonalni trokut netetivnog četvreovrha u izotropnoj ravnini
KoG, 2021 Geometry of the non cyclic quadrangle in the isotropic plane was introduced in [2] and [6]. Herein, its diagonal triangle is studied and some nice properties of it are given.
Marija Šimić Horvath, Vladimir Volenec
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Sums of Diagonals in Pascal’s Triangle
Mathematics ExchangeWe analyze sums of entries on diagonals of integer slope in Pascal’s triangle, obtain a recurrence relation that these diagonal sums obey, and compute their generating function. We use the generating function to approximate the exponential growth of the diagonal sums.
Jamisen McCrary, Russell May
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Diagonal triangle of a non-tangential quadrilateral in the isotropic plane
Mathematical Communications, 2011 Properties of the non-tangential quadrilateral $\lijepoa \lijepob \lijepoc \lijepod$ in the isotropic plane concerning its diagonal triangle are given in this paper. A quadrilateral is called standard if a parabola with the equation $x=y^2$ is inscribed in it. Every non-tangential quadrilateral can be represented in the standard position.
Šimić Horvath, Marija +2 more
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Growth of periodic orbits and generalized diagonals for typical triangular billiards
Journal of Modern Dynamics, 2013 minor corrections have been made and some bibliography ...
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On Generating functions of Diagonals Sequences of Sheffer and Riordan Number Triangles
, 2017 9 ...
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Projective Parameterization of Moving Diagonal Triangles on the Null Conic via the Cayley Transform
This paper develops a finitist and fully algebraic framework for the projective parameterization of moving diagonal triangles generated by a null quadrangle in Universal Hyperbolic Geometry (UHG). Starting from a fixed nil triangle and a fourth moving null point on the absolute null conic, the paper derives explicit rational coordinate trajectories for
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On curves of the third degree which goes through apexes of a complete tetragon and its diagonal triangle [PDF]
Časopis pro pěstování matematiky a fysiky, 1887 openaire +1 more source
ApSimon's Diagonal Point Triangle Problem
American Mathematical Monthly, 1997Richard K Guy
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