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Interior angle sums of geodesic triangles in S2XR and H2XR geometries
Authors: Jenö Szirmai
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Abstract
In the present paper we study $\SXR$ and $\HXR$ geometries, which are homogeneous Thurston 3-geometries. We analyse the interior angle sums of geodesic triangles in both geometries and we prove that in $\SXR$ space it can be larger than or equal to $\pi$ and in $\HXR$ space the angle sums can be less than or equal to $\pi$. % This proof is a new direct approach to the issue and it is based on the projective model of $\SXR$ and $\HXR$ geometries described by E. Moln\'ar in \cite{M97}.Budapest University of Technology and
Economics Institute of Mathematics,
Department of Geometry,
Budapest, P. O. Box: 91, H-1521
E-mail:
Economics Institute of Mathematics,
Department of Geometry,
Budapest, P. O. Box: 91, H-1521
E-mail:
Fulltext
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Contents
- New Form of the Hidden Logarithm Problem and its Algebraic Support
- Inequalities of Hermite-Hadamard Type for K-Bounded Modulus Convex Complex Functions
- Commutative Weakly Tripotent Group Rings
- Isohedral tilings for hyperbolic translation group of genus two which admit additional isometries
- Interior angle sums of geodesic triangles in S2XR and H2XR geometries
- Signature Schemes on Algebras, Satisfying Enhanced Criterion of Post-quantum Security
- Quasi-Kählerian manifolds and quasi-Sasakian hypersurfaces axiom
- Laurent-Padé approximation for locating singularities of meromorphic functions with values given on simple closed contours
- Asymmetric Separation of Convex Sets
