scholarly journals Magnetic Jacobi Fields in 3-Dimensional Cosymplectic Manifolds

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3220
Author(s):  
Marian Ioan Munteanu ◽  
Ana Irina Nistor
Keyword(s):  
Magnetic Fields ◽  
Euclidean Space ◽  
Product Spaces ◽  
Jacobi Fields ◽  
3 Dimensional ◽  
Cosymplectic Manifolds

We classify the magnetic Jacobi fields in cosymplectic manifolds of dimension 3, enriching the results in the study of magnetic Jacobi fields derived from uniform magnetic fields. In particular, we give examples of Jacobi magnetic fields in the Euclidean space E3 and we conclude with the description of magnetic Jacobi fields in the product spaces S2×R and H2×R.

scholarly journals CURVES ON RULED SURFACES UNDER INFINITESIMAL BENDING

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Marija Najdanović ◽  
Miroslav Maksimović ◽  
Ljubica Velimirović
Keyword(s):  
Euclidean Space ◽  
Ruled Surfaces ◽  
Dimensional Euclidean Space ◽  
Hyperbolic Paraboloid ◽  
3 Dimensional ◽  
Infinitesimal Bending

Infinitesimal bending of curves lying with a given precision on ruled surfaces in 3-dimensional Euclidean space is studied. In particular, the bending of curves on the cylinder, the hyperbolic paraboloid and the helicoid are considered and appropriate bending fields are found. Some examples are graphically presented.

Complete 3-dimensional λ-translators in the Euclidean space ℝ4

2021 ◽  
pp. 1-54
Author(s):  
Zhi Li ◽  
Guoxin Wei ◽  
Gangyi Chen
Keyword(s):  
Euclidean Space ◽  
Fundamental Form ◽  
Second Fundamental Form ◽  
3 Dimensional ◽  
The Second Fundamental Form

In this paper, we obtain the classification theorems for 3-dimensional complete [Formula: see text]-translators [Formula: see text] with constant squared norm [Formula: see text] of the second fundamental form and constant [Formula: see text] in the Euclidean space [Formula: see text].

Ricci solitons on 3-dimensional cosymplectic manifolds

2017 ◽  
Vol 67 (4) ◽  
Author(s):  
Yaning Wang
Keyword(s):  
Ricci Solitons ◽  
Cosymplectic Manifold ◽  
3 Dimensional ◽  
Cosymplectic Manifolds

AbstractIn this paper, we prove that if a 3-dimensional cosymplectic manifold

scholarly journals On Various Definitions of Capacity and Related Notions

1967 ◽  
Vol 30 ◽  
pp. 121-127 ◽  
Author(s):  
Makoto Ohtsuka
Keyword(s):  
Euclidean Space ◽  
Positive Charge ◽  
Dimensional Euclidean Space ◽  
3 Dimensional ◽  
Electric Capacity ◽  
De La Vallée Poussin

The electric capacity of a conductor in the 3-dimensional euclidean space is defined as the ratio of a positive charge given to the conductor and the potential on its surface. The notion of capacity was defined mathematically first by N. Wiener [7] and developed by C. de la Vallée Poussin, O. Frostman and others. For the history we refer to Frostman’s thesis [2]. Recently studies were made on different definitions of capacity and related notions. We refer to M. Ohtsuka [4] and G. Choquet [1], for instance. In the present paper we shall investigate further some relations among various kinds of capacity and related notions. A part of the results was announced in a lecture of the author in 1962.

Vector sums of Valentine convex sets

1982 ◽  
Vol 92 (1) ◽  
pp. 17-19
Author(s):  
H. G. Eggleston
Keyword(s):  
Euclidean Space ◽  
Convex Sets ◽  
Convex Set ◽  
Dimensional Space ◽  
End Points ◽  
3 Dimensional ◽  
Vector Sum ◽  
Open Question

SummaryA set X in Euclidean space is Valentine n–convex, or simply n–convex' if it has the following property. If X contains a subset Y consisting of n distinct points then X also contains the points of at least one segment with end points in Y. We show here that the vector sum of two plane compact 3-convex sets is 5-convex (which complements the result of I. D. Calvert(1) that the intersection of two plane compact 3-convex sets is 5-convex) and that the vector sum of a plane connected compact 3-convex set with itself is 4-convex. These results are not true in 4 dimensional space. It is an open question whether or not they are true in 3-dimensional space.

scholarly journals Surfaces of Finite III-type

2021 ◽  
Vol 15 ◽  
pp. 190-194
Author(s):  
Hassan Al-Zoubi
Keyword(s):  
Euclidean Space ◽  
Fundamental Form ◽  
Principal Curvature ◽  
Gauss Curvature ◽  
Dimensional Euclidean Space ◽  
Surfaces Of Revolution ◽  
3 Dimensional ◽  
The Third ◽  
Third Fundamental Form ◽  
Special Case

In this paper, we consider surfaces of revolution in the 3-dimensional Euclidean space E3 with nonvanishing Gauss curvature. We introduce the finite Chen type surfaces with respect to the third fundamental form of the surface. We present a special case of this family of surfaces of revolution in E3, namely, surfaces of revolution with R is constant, where R denotes the sum of the radii of the principal curvature of a surface.

scholarly journals On the second Gaussian curvature of ruled surfaces in Euclidean $3$-space

2006 ◽  
Vol 37 (3) ◽  
pp. 221-226 ◽  
Author(s):  
Dae Won Yoon
Keyword(s):  
Euclidean Space ◽  
Gaussian Curvature ◽  
Mean Curvature ◽  
Ruled Surface ◽  
Ruled Surfaces ◽  
Dimensional Euclidean Space ◽  
3 Dimensional ◽  
The Mean ◽  
Second Gaussian Curvature

In this paper, we mainly investigate non developable ruled surface in a 3-dimensional Euclidean space satisfying the equation $K_{II} = KH$ along each ruling, where $K$ is the Gaussian curvature, $H$ is the mean curvature and $K_{II}$ is the second Gaussian curvature.

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