quaternionic space
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2021 ◽  
Vol 46 (1) ◽  
pp. 71-83
Author(s):  
Tuba Ağirman Aydin ◽  
Rabil Ayazoğlu ◽  
Hüseyin Kocayiğit

Abstract The curves of constant width are special curves used in engineering, architecture and technology. In the literature, these curves are considered according to different roofs in different spaces and some integral characterizations of these curves are obtained. However, in order to examine the geometric properties of curves of constant width, more than characterization is required. In this study, firstly differential equations characterizing quaternionic space curves of constant width are obtained. Then, the approximate solutions of the differential equations obtained are calculated by the Morgan-Voyce polynomial approach.The geometric properties of this curve type are examined with the help of these solutions.



Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 480 ◽  
Author(s):  
Gabriel Macsim ◽  
Adela Mihai ◽  
Ion Mihai

In the geometry of submanifolds, Chen inequalities represent one of the most important tool to find relationships between intrinsic and extrinsic invariants; the aim is to find sharp such inequalities. In this paper we establish an optimal inequality for the Chen invariant δ ( 2 , 2 ) on Lagrangian submanifolds in quaternionic space forms, regarded as a problem of constrained maxima.



2019 ◽  
Vol 125 (2) ◽  
pp. 24002 ◽  
Author(s):  
S. B. Tabeu ◽  
F. Fotsa-Ngaffo ◽  
A. Kenfack-Jiotsa




2018 ◽  
Vol 26 (3) ◽  
pp. 181-196 ◽  
Author(s):  
Gabriel Macsim ◽  
Adela Mihai

AbstractWe establish an inequality for an intrinsic invariant of Chen-type defined on quaternionic CR-submanifolds in quaternionic space forms, in terms of the squared mean curvature, the main extrinsic invariant, by using the method of constrained extrema.



2018 ◽  
Vol 30 (3) ◽  
pp. 785-798
Author(s):  
José Carmelo González-Dávila

AbstractWe construct special classes of totally geodesic almost regular foliations, namely, complex radial foliations in Hermitian manifolds and quaternionic radial foliations in quaternionic Kähler manifolds, and we give criteria for their harmonicity and minimality. Then examples of these foliations on complex and quaternionic space forms, which are harmonic and minimal, are presented.



2016 ◽  
Vol 8 (2) ◽  
pp. 271-281
Author(s):  
Z. Nazari ◽  
E. Abedi

Abstract The purpose of this paper is to study Ricci solitons on QR-hypersurfaces M of a quaternionic space form ℚn such that the shape operator A with respect to N has one eigenvalue. We prove that Ricci soliton on QR-hypersurfaces M with eigenvalue zero is steady and for eigenvalue nonzero is shrinking.



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