Related papers: Loxodromes on Twisted Surfaces in Lorentz-Minkowsk…
In the present paper, loxodromes, which cut all meridians and parallels of twisted surfaces (that can be considered as a generalization of rotational surfaces) at a constant angle, have been studied in Euclidean 3-space and some examples…
In this paper, we examine timelike loxodromes on three kinds of Lorentzian helicoidal surfaces in Minkowski $n$--space. First, we obtain the first order ordinary differential equations which determine timelike loxodromes on the Lorentzian…
In this paper, we obtain the differential equations of the space-like loxodromes on the non-degenerate canal surfaces depending on the causal characters of these canal surfaces and their meridians in Minkowski 3-space. Also we give an…
In this paper, we prove important results concerning the loxodromes on an invariant surface in a three-dimensional Riemannian manifold, some of which generalize classical results about loxodromes on rotational surfaces in $\mathbb{R}^3$. In…
In this paper, we study on the characterizations of loxodromes on the rotational surfaces satisfying some special geometric properties such as having constant Gaussian curvature, flat and minimality in Euclidean 3-space. First, we give the…
In this paper, we study three types of helicoidal surfaces in a Lorentzian n--space $\mathbb{E}^n_1$. First, we find the parametrizations of spacelike loxodromes on such spacelike helicoidal surfaces in $\mathbb{E}^n_1$. Then, we make a…
Special curves and surfaces have an important place in mathematics, engineering and other fields of science. Loxodromes are special curves which cut all meridians on the Earth's surface at a constant angle and they are very popular in…
Spacelike surfaces in the Lorentz-Minkowski space L^3 can be endowed with two different Riemannian metrics, the metric inherited from L^3 and the one induced by the Euclidean metric of R^3. It is well known that the only surfaces with zero…
We review part of the classical theory of curves and surfaces in $3$-dimensional Lorentz-Minkowski space. We focus in spacelike surfaces with constant mean curvature pointing the differences and similarities with the Euclidean space.
We give a systematic method to calculate some homological data from the global monodromy of a topological elliptic surface. We apply this method to the cases 1) the transcendental lattice of an extremal elliptic K3 surface, 2) the torsion…
In this paper, we define two types of helicoidal surfaces of non-lightlike frontals in Lorentz-Minkowski 3-space and investigate when they become lightcone framed base surfaces. Moreover, by constructing appropriate diffeomorphic…
In this study, we consider the notion of similar ruled surface for timelike and spacelike ruled surfaces in Minkowski 3-space. We obtain some properties of these special surfaces in E_1^3 and we show that developable ruled surfaces in E_1^3…
In this paper, we study relatively normal-slant helices lying on timelike as well as spacelike surfaces in Minkowski $3$-space $ \mathbb{E}_1^3$. The axes of spacelike and timelike relatively normal-slant helices are obtained via their…
Motivated by the relation between (twisted) K3 surfaces and special cubic fourfolds, we construct moduli spaces of polarized twisted K3 surfaces of any fixed degree and order. We do this by mimicking the construction of the moduli space of…
The geometry and topology of complete nonorientable maximal surfaces with lightlike singularities in the Lorentz-Minkowski 3-space are studied. Some topological congruence formulae for surfaces of this kind are obtained. As a consequence,…
Kenmotsu's formula describes surfaces in Euclidean 3-space by their mean curvature functions and Gauss maps. In Lorentzian 3-space, Akutagawa-Nishikawa's formula and Magid's formula are Kenmotsu-type formulas for spacelike surfaces and for…
In this paper, we consider the differential geometry properties of focal surfaces of lightcone framed surfaces in Lorentz-Minkowski 3-space. In general, a mixed type surface is a connected regular surface with non-empty spacelike and…
In this paper we characterize concircular helices in $R^3$ by means of a differential equation involving their curvature and torsion. We find a full description of concircular surfaces in $R^3$ as a special family of ruled surfaces, and we…
A connected regular surface in Lorentz-Minkowski 3-space is called a mixed type surface if the spacelike, timelike and lightlike point sets are all non-empty. Lightlike points on mixed type surfaces may be regarded as singular points of the…
We first describe the numerical invariants attached to the second fundamental form of a spacelike surface in four-dimensional Minkowski space. We then study the configuration of the nu-principal curvature lines on a spacelike surface, when…