Meridian surfaces in the Euclidean 4-space are two-dimensional surfaces which are one-parameter systems of meridians of a standard rotational hypersurface. On the base of our invariant theory of surfaces we study meridian surfaces with special invariants. In the present paper we give the complete classification of Chen…
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48 results for “Meridian Surfaces”
The study classifies timelike meridian surfaces in Minkowski 4-space.
problem Characterizing timelike meridian surfaces in Minkowski space.
method Analyzing surfaces as one-parameter systems of meridians of rotational hypersurfaces.
result Classification of timelike meridian surfaces with various curvature properties.
We consider a special class of spacelike surfaces in the Minkowski 4-space which are one-parameter systems of meridians of the rotational hypersurface with timelike or spacelike axis. We call these surfaces meridian surfaces of elliptic or hyperbolic type, respectively. On the base of our invariant theory of surfaces w…
The study classifies special spacelike surfaces in Minkowski 4-space.
problem Classifying meridian surfaces in Minkowski space.
method Constructing and classifying meridian surfaces of parabolic type with specific curvature properties.
result Complete classification of meridian surfaces of parabolic type with constant Gauss or mean curvature.
The study classifies meridian surfaces with specific curvature properties in a special 4D space.
problem Characterizing surfaces with parallel mean or normalized mean curvature vectors.
method Classification of meridian surfaces based on curvature properties.
result Existence of surfaces with parallel normalized mean curvature but not mean curvature.
Meridian Surfaces with Constant Mean Curvature in Pseudo-Euclidean 4-space with Neutral Metricmath.DG
The study classifies meridian surfaces with constant mean curvature in a special pseudo-Euclidean space.
problem Classifying meridian surfaces with constant mean curvature in a pseudo-Euclidean space.
method Analyzing one-parameter systems of meridians of rotational hypersurfaces in a four-dimensional pseudo-Euclidean space with neutral metric.
result Complete classification of meridian surfaces with constant mean curvature, including minimal and quasi-minimal surfaces.
The study classifies special Lorentz surfaces in a 4-space with neutral metric.
problem Classifying meridian surfaces in a pseudo-Euclidean 4-space.
method Constructing and classifying meridian surfaces with specific properties.
result There exist meridian surfaces with parallel normalized mean curvature vector field but not parallel mean curvature vector.
In the present article we study a special class of surfaces in the four-dimensional Euclidean space, which are one-parameter systems of meridians of the standard rotational hypersurface. They are called meridian surfaces. We show that a meridian surface has a harmonic Gauss map if and only if it is part of a plane. Fur…
Meridian lemma extended to fully alternating links in thickened surfaces.
problem Extending Menasco's meridian lemma to fully alternating links in thickened surfaces.
method Developed a new meridian lemma for fully alternating links in thickened orientable surfaces of positive genus.
result The meridian lemma holds for fully alternating links in thickened surfaces.
In the present article we study a special class of surfaces in the four-dimensional Euclidean space, which are one-parameter systems of meridians of the standard rotational hypersurface. They are called meridian surfaces. We classified semi-parallel meridian surface in 4-dimensional Euclidean space .
In the present paper we consider a special class of spacelike surfaces in the Minkowski 4-space which are one-parameter systems of meridians of the rotational hypersurface with timelike or spacelike axis. They are called meridian surfaces of elliptic or hyperbolic type, respectively. We study these surfaces with respec…
Marginally trapped meridian surfaces of parabolic type in the four-dimensional Minkowski spacemath.DG
A marginally trapped surface in the four-dimensional Minkowski space is a spacelike surface whose mean curvature vector is lightlike at each point. We introduce meridian surfaces of parabolic type as one-parameter systems of meridians of a rotational hypersurface with lightlike axis in Minkowski 4-space and find their …
In this paper, we study meridian surfaces of Weingarten type in Euclidean 4-space E^4. We give the neccessary and sufficient conditions for a meridian surface in E^4 to become Weingarten type.
Study timelike meridian surfaces in Minkowski 4-space with specific properties.
problem Characterize timelike meridian surfaces with special properties in Minkowski 4-space.
method Analyze different classes of timelike meridian surfaces with constant Gauss curvature, mean curvature, and parallel normalized mean curvature vector field.
result Explicit solutions to PDEs describing timelike surfaces with parallel normalized mean curvature vector field.
Surface-links with specific groups are always trivial.
problem Understanding when surface-links are trivial.
method Analyzing surface-links with meridian-based free fundamental groups.
result Disconnected surface-links with meridian-based free fundamental groups are trivial.
The study bounds knot lengths and volumes using essential surfaces.
problem Estimating the lengths and volumes of hyperbolic knots.
method Using essential surfaces to derive bounds on meridian length and cusp volume.
result New upper bounds on meridian length and cusp volume for hyperbolic knots.
We apply the invariant theory of surfaces in the four-dimensional Euclidean space to the class of general rotational surfaces with meridians lying in two-dimensional planes. We find all minimal super-conformal surfaces of this class.
A marginally trapped surface in the four-dimensional Minkowski space is a spacelike surface whose mean curvature vector is lightlike at each point. We associate a geometrically determined moving frame field to such a surface and using the derivative formulas for this frame field we obtain seven invariant functions. Our…
The paper studies loxodromes on twisted surfaces in a specific 3D space.
problem Analyzing loxodromes on twisted surfaces in Lorentz-Minkowski 3-space.
method Developed general formulas and differential equations for different types of loxodromes, meridians, and surfaces in E^3_1.
result Generalized differential equations for loxodromes on Type-I, Type-II, and Type-III twisted surfaces.
The study defines new surfaces with specific cut locus properties and provides conditions for their existence.
problem Understanding the properties of surfaces of revolution with specific cut locus structures.
method Analyzing the Gaussian curvature function and proving conditions for surfaces to be generalized von Mangoldt.
result For any surface of revolution with finite total curvature, there exists a generalized von Mangoldt surface with the same total curvature and non-monotone Gaussian curvature function along a meridian.
It is a well-known procedure for constructing a torus knot or link that first we prepare an unknotted torus and meridian disks in the complementary solid tori of it, and second smooth the intersections of the boundary of meridian disks uniformly. Then we obtain a torus knot or link on the unknotted torus and its Seifer…
Study on cut locus structure of a specific Randers surface.
problem Analyzing the cut locus of a Randers rotational 2-sphere.
method Examined Gaussian curvature monotonicity and its effect on cut locus.
result Cut locus properties depend on Gaussian curvature monotonicity.
Study on generalized spherical surfaces in Euclidean spaces.
problem Characterizing and analyzing generalized spherical surfaces in Euclidean spaces.
method Investigation of generalized spherical curves and surfaces in Euclidean spaces, calculation of curvatures.
result Identification and characterization of different types of generalized spherical surfaces in Euclidean spaces.
In this paper, we show that the constant property of the Gaussian curvature of surfaces of revolution in both and depend only on the radius of rotation. We then give necessary and sufficient conditions for the Gaussian curvature of the general rotational surfaces whose meridians lie in two…
New 2-spheres of revolution with simple cut locus structures.
problem Determining surfaces of revolution with simple cut locus structures.
method Introducing a new family of 2-spheres of revolution.
result The new family {M_n}_n has a simple cut locus structure.
Surfaces with Parallel Normalized Mean Curvature Vector Field in Euclidean or Minkowski 4-Spacemath.DG
Study surfaces with parallel mean curvature in 4D spaces.
problem Characterize surfaces with parallel normalized mean curvature in Euclidean or Minkowski 4-space.
method Introduced special isothermal parameters and described surfaces using invariant functions.
result Surfaces with parallel normalized mean curvature are uniquely determined by three invariant functions.
The paper refines triple linking numbers and connects them to surface systems.
problem Understanding the relationship between triple linking numbers and surface systems.
method Analyzing the homeomorphic surface systems and using group theory properties.
result Conditions for homeomorphic surface systems are equivalent to refined triple linking numbers.
Computes extendable mapping classes for knotted surfaces in .
problem Computing extendable mapping classes for knotted surfaces in .
method Using ordinary untwisted rim surgery and meridian-longitude rigidity conditions on knot groups.
result Exact computation of extendable mapping classes for specific knotted surfaces.
Complex of separating meridians can be extended to all meridians in genus ≥6 handlebodies.
problem Extending automorphisms of separating meridians to all meridians in handlebodies.
method Showing every automorphism of the complex of separating meridians can be extended to an automorphism on the complex of all meridians.
result Automorphisms of separating meridians can be extended to all meridians in handlebodies of genus ≥6.
Study of loxodromes on twisted surfaces in 3D space.
problem Characterizing loxodromes on surfaces with varying curvature.
method Analysis of loxodromes on twisted surfaces in Euclidean 3-space.
result Construction of examples to visualize loxodromes on twisted surfaces.
Infinite Klein bottles with 4-fold meridians found.
problem Finding indecomposable Klein bottles with specific meridian orders.
method Exhibited an infinite family of Klein bottles in 4-sphere.
result Infinite family of indecomposable Klein bottles with order-4 meridians.
Study space-like loxodromes on canal surfaces in Minkowski 3-space.
problem Characterizing space-like loxodromes on canal surfaces.
method Solving differential equations for space-like loxodromes on canal surfaces in Minkowski 3-space.
result Differential equations for space-like loxodromes on canal surfaces.
The aim of this paper is to determine the structure of the cut locus for a class of surfaces of revolution homeomorphic to a cylinder. Let denote a cylinder of revolution which admits a reflective symmetry fixing a parallel called the equator of It will be proved that the cut locus of a point of is a s…
Smooth maps preserve distances on specific revolution surfaces.
problem Existence of smooth maps on revolution surfaces.
method Proving existence of maps preserving distances on meridians and parallels.
result Smooth maps exist from revolution surfaces to Euclidean plane.
The paper explores meridional ranks of knotted surfaces and welded knots, proving equalities and relationships.
problem Investigating the Meridional Rank Conjecture for knotted surfaces and welded knots.
method Constructing knots with specific properties, establishing equalities, and using Tube map.
result Established the equality of bridge number and meridional rank for certain knots and knotted spheres.
Examines how meridians and parallels help in map drawing.
problem Understanding map drawing and foliations of the sphere.
method Analyzes Euler's work on cartography and meridians/parallels.
result Meridians and parallels are crucial for map drawing.
Suppose a genus two handlebody is removed from a 3-manifold M and then a single meridian of the handlebody is restored. The result is a knot or link complement in M and it is natural to ask whether geometric properties of the link complement say something about the meridian that was restored. Here we consider what the …
Data structure for Heegaard splittings reduces complexity.
problem Representing Heegaard splittings efficiently.
method Data structure for normal curves with respect to triangulations.
result Exponential gains in space complexity for certain families.
Study stabilizers in handlebody group; meridians are undistorted, others are exponentially distorted.
problem Geometric properties of stabilizers in handlebody group.
method Analysis of stabilizers of meridians and primitive curves/annuli.
result Stabilizers of meridians are undistorted, others are exponentially distorted.
Study on surfaces in pseudo-Euclidean space with neutral metric.
problem Characterizing surfaces in pseudo-Euclidean 4-space with neutral metrics.
method Defined and studied Lorentz general rotational surfaces with specific properties.
result Complete classification of various types of general rotational surfaces.
We consider non-orientable closed surfaces of minimum crosscap number in the -lens space , where and are solid tori. Bredon and Wood gave a formula for calculating the minimum crosscap number. Rubinstein showed that with even has only one isotopy cla…
Characterizes alternating knot exteriors using special surfaces.
problem Understanding topological properties of alternating knots.
method Topological characterisation using special spanning surfaces and a normal surface algorithm.
result Alternating is a topological property of knot exteriors, not just diagrams.
Prove integrality of genus- indices with adjoint Reidemeister torsions for twist knots and meridians.
problem Prove integrality of genus- indices with adjoint Reidemeister torsions for twist knots and meridians.
method Consider the sum of the adjoint Reidemeister torsions and prove integrality for twist knots and meridians.
result Prove integrality of genus- indices with adjoint Reidemeister torsions for twist knots and meridians.
Basic Classes of Timelike General Rotational Surfaces in the Four-dimensional Minkowski Spacemath.DG
Study of timelike surfaces in Minkowski space with specific geometric properties.
problem Characterizing geometric properties of timelike surfaces in Minkowski space.
method Analytical study of two types of timelike general rotational surfaces.
result Explicit descriptions of minimal and surfaces with specific curvature properties.
This note proves properties of surface-links with trivial components.
problem Properties of surface-links with trivial components.
method Analyzes closed oriented disconnected surfaces and their links.
result For certain surface-links, trivial components result in ribbon links.
The paper studies timelike loxodromes on specific Lorentzian helicoidal surfaces.
problem Analyzing timelike loxodromes on Lorentzian helicoidal surfaces.
method First-order differential equations, general solutions, explicit parametrizations.
result Explicit parametrizations of timelike loxodromes on Lorentzian helicoidal surfaces.
New mapping classes of knotted surfaces are computed via surgery.
problem Computing extendable mapping classes of knotted surfaces after surgery.
method Using ordinary untwisted rim surgery, compute the exact extendable mapping-class subgroup.
result The extendable mapping-class subgroup is computed precisely.
New foliations show knot meridians are detectable.
problem Detecting knots in 3-manifolds.
method Constructing co-oriented taut foliations intersecting knot meridians.
result Evidence supports conjecture related to L-space conjecture.