Morgan-Voyce Polynomial Approach for Quaternionic Space Curves of Constant Width

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.

δ(2,2)-Invariant for Lagrangian Submanifolds in Quaternionic Space Forms

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.

An Inequality on Quaternionic CR-Submanifolds

We 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.

Harmonicity and minimality of complex and quaternionic radial foliations

We 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.

Ricci solitons on QR-hypersurfaces of a quaternionic space form ℚn

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.