Related papers: On the Quaternionic Involute-Evolute Curves
We consider curves which go around Whitney umbrella. Then we consider the geodesic and the normal curvatures, ruled surfaces generated by the normal vector and normal developable surfaces with respect to the tangent and bi-tangent vectors…
The orthogonal trajectories of the first tangents of the curve are called the involutes of $x$. The hyperspheres which have higher order contact with a curve $x$ are known osculating hyperspheres of $x$. The centers of osculating…
In this work, first, we express some characterizations of helices and ccr curves in the Euclidean 4-space. Thereafter, relations among Frenet-Serret invariants of Bertrand curve of a helix are presented. Moreover, in the same space, some…
Numerous attempts have been made to replicate the success of complex-valued algebra in engineering and science to other hypercomplex domains such as quaternions, tessarines, biquaternions, and octonions. Perhaps, none have matched the…
Motivated by a model in quantum computation we study orthogonal sets of integral vectors of the same norm that can be extended with new vectors keeping the norm and the orthogonality. Our approach involves some arithmetic properties of the…
We present a construction of new invariant sets for fibred polynomial dynamics with base an irrational rotation over the unit circle, called multi-curves. Furthermore, the local dynamical theory for attracting invariant curves is extended…
Based on a new generalization of Cauchy-Riemann system presented in this paper, we introduce a class of quaternion-valued functions of a quaternionic variable, which are called algebraic regular functions. The set of algebraic regular…
A quaternionic calculus for surface pairs in the conformal 4-sphere is elaborated. This calculus is then used to discuss the relation between curved flats in the symmetric space of point pairs and Darboux and Christoffel pairs of isothermic…
We study the quantum invariants of projective varieties over the number fields. Namely, explicit formulas for a functor $\mathscr{Q}$ on such varieties are proved. The case of abelian varieties with complex multiplication is treated in…
A survey of properties of a sequence of coefficients appearing in the evaluation of a quartic definite integral is presented. These properties are of analytical, combinatorial and number-theoretical nature.
In this paper, we investigate geometric properties of some curvature tensors of a four-dimensional Walker manifold. Some characterization theorems are also obtained.
Several sets of quaternionic functions are described and studied. Residue current of the right inverse of a quaternionic function is introduced in particular cases.
In this paper, we investigate some interesting properties of q-Berstein polynomials realted to q-Euler numbers by using the fermionic q-integral on Zp.
These lectures give a short introduction to the study of curves on algebraic varieties. After an elementary proof of the dimension formula for the space of curves, we summarize the basic properties of uniruled and of rationally connected…
An involution is usually defined as a mapping that is its own inverse. In this paper, we study quaternion involutions that have the additional properties of distribution over addition and multiplication. We review formal axioms for such…
Let $K$ be an imaginary quadratic field. Modular forms for GL(2) over $K$ are known as Bianchi modular forms. Standard modularity conjectures assert that every weight 2 rational Bianchi newform has either an associated elliptic curve over…
In this paper we investigate some interesting formulae of q-Euler numbers and polynomials related to the modified q-Bernstein polynomials.
In this paper, we extend the method developed in [17, 18] to curves in the Minkowski plane. The method proposes a way to study deformations of plane curves taking into consideration their geometry as well as their singularities. We deal in…
We give some methods for computing equations for certain Shimura curves, natural maps between them, and special points on them. We then illustrate these methods by working out several examples in varying degrees of detail. For instance, we…
This chapter reviews some past and recent developments in shape comparison and analysis of curves based on the computation of intrinsic Riemannian metrics on the space of curves modulo shape-preserving transformations. We summarize the…