Interior angle sums of geodesic triangles in S2×R and H2×R geometries
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SZIRMAI, Jeno. Interior angle sums of geodesic triangles in S2×R and H2×R geometries. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2020, nr. 2(93), pp. 44-61. ISSN 1024-7696.
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
Numărul 2(93) / 2020 / ISSN 1024-7696 /ISSNe 2587-4322

Interior angle sums of geodesic triangles in S2×R and H2×R geometries

CZU: 514.13+514.772.22+528.3
MSC 2010: 53A20, 53A35, 52C35, 53B20.

Pag. 44-61

Szirmai Jeno
 
Budapest University of Technology and Economics, Budapest
 
 
Disponibil în IBN: 18 septembrie 2020


Rezumat

In the present paper we study S2×R and H2×R geometries, which are homogeneous Thurston 3-geometries. We analyse the interior angle sums of geodesic triangles in both geometries and we prove that in S2×R space it can be larger than or equal to  and in H2×R space the angle sums can be less than or equal to . This proof is a new direct approach to the issue and it is based on the projective model of S2×R and H2×R geometries described by E. Moln´ar in [7].

Cuvinte-cheie
Thurston geometries, S²×R, H²×R geometries, geodesic triangles, interior angle sum

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<dc:creator>Szirmai, J.</dc:creator>
<dc:date>2020-09-18</dc:date>
<dc:description xml:lang='en'><p>In the present paper we study S<sup>2</sup>&times;R and H<sup>2</sup>&times;R geometries, which are homogeneous Thurston 3-geometries. We analyse the interior angle sums of geodesic triangles in both geometries and we prove that in S<sup>2</sup>&times;R space it can be larger than or equal to  and in H<sup>2</sup>&times;R space the angle sums can be less than or equal to . This proof is a new direct approach to the issue and it is based on the projective model of S<sup>2</sup>&times;R and H<sup>2</sup>&times;R geometries described by E. Moln&acute;ar in [7].</p></dc:description>
<dc:source>Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica 93 (2) 44-61</dc:source>
<dc:subject>Thurston geometries</dc:subject>
<dc:subject>S²×R</dc:subject>
<dc:subject>H²×R geometries</dc:subject>
<dc:subject>geodesic
triangles</dc:subject>
<dc:subject>interior angle sum</dc:subject>
<dc:title>Interior angle sums of geodesic triangles in S2&times;R and H2&times;R geometries</dc:title>
<dc:type>info:eu-repo/semantics/article</dc:type>
</oai_dc:dc>