scholarly journals Osculating curves in 4-dimensional semi-Euclidean space with index 2

2017 ◽  
Vol 15 (1) ◽  
pp. 562-567
Author(s):  
Kazim İlarslan ◽  
Nihal Kiliç ◽  
Hatice Altin Erdem
Keyword(s):  
Euclidean Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Euclidian Space ◽  
Null Curves ◽  
Index 2 ◽  
Necessary And Sufficient

Abstract In this paper, we give the necessary and sufficient conditions for non-null curves with non-null normals in 4-dimensional Semi-Euclidian space with indeks 2 to be osculating curves. Also we give some examples of non-null osculating curves in $\mathbb{E}_{2}^{4}$ .

scholarly journals Special Curves According to Bishop Frame in Minkowski 3-Space

2020 ◽  
Vol 5 (1) ◽  
pp. 237-248
Author(s):  
Muhammad Abubakar Isah ◽  
Mihriban Alyamaç Külahçı
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Bishop Frame ◽  
Null Curve ◽  
Minkowski Spaces ◽  
Slant Helix ◽  
Null Curves ◽  
Necessary And Sufficient

AbstractPseudo null curves were studied by some geometers in both Euclidean and Minkowski spaces, but some special characters of the curve are not considered. In this paper, we study weak AW (k) – type and AW (k) – type pseudo null curve in Minkowski 3-space [E_1^3 . We define helix and slant helix according to Bishop frame in [E_1^3 . Furthermore, the necessary and sufficient conditions for the slant helix and helix in Minkowski 3-space are obtained.

scholarly journals A New Approach to Mannheim Curve in Euclidean 3-Space

2021 ◽  
Vol 54 ◽  
Author(s):  
Ali UÇUM ◽  
Çetin Camcı ◽  
Kazım İlarslan
Keyword(s):  
Euclidean Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Dimensional Euclidean Space ◽  
New Approach ◽  
3 Dimensional ◽  
Mannheim Curve ◽  
Necessary And Sufficient

In this article, a new approach is given for Mannheim curves in 3-dimensional Euclidean space. Thanks to this approach, the necessary and sufficient conditions including the known results have been obtained for a curve to be Mannheim curve in E³. In addition, related examples and graphs are given by showing that there can be Mannheim curves in Salkowski or anti-Salkowski curves as well as giving Mannheim mate curves, which are not in literature. Finally, the Mannheim partner curves are characterized in E³.

scholarly journals Semi-symmetry of δ(2,2) Chen ideal submanifolds

Filomat ◽  
2015 ◽  
Vol 29 (3) ◽  
pp. 393-400
Author(s):  
Anica Pantic ◽  
Miroslava Petrovic-Torgaseva
Keyword(s):  
Euclidean Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient

In this paper we discuss ?(2,2) Chen ideal submanifolds M4 in the Euclidean space E6, and we find the necessary and sufficient conditions under which such a submanifold M4 is semi-symmetric, i.e. it satisfies the condition R(X,Y)? R = 0.

Hypersurfaces of Euclidean Space as Gradient Ricci Solitons

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
Hana Al-Sodais ◽  
Haila Alodan ◽  
Sharief Deshmukh
Keyword(s):  
Euclidean Space ◽  
Sufficient Conditions ◽  
Ricci Soliton ◽  
Necessary And Sufficient Conditions ◽  
Ricci Solitons ◽  
Gradient Ricci Soliton ◽  
Gradient Ricci Solitons ◽  
Necessary And Sufficient

Abstract In this paper we obtain some necessary and sufficient conditions for a hypersurface of a Euclidean space to be a gradient Ricci soliton. We also study the geometry of a special type of compact Ricci solitons isometrically immersed into a Euclidean space.

Immersing projective spaces in Euclidean space

1991 ◽  
Vol 117 (1-2) ◽  
pp. 155-170 ◽  
Author(s):  
M. C. Crabb
Keyword(s):  
Euclidean Space ◽  
Sufficient Conditions ◽  
Projective Spaces ◽  
Necessary And Sufficient Conditions ◽  
Obstruction Theory ◽  
Real Dimension ◽  
Complex Projective Spaces ◽  
L 14 ◽  
Necessary And Sufficient ◽  
Complex Projective

SynopsisUsing the KOℝ/2-theoretic obstruction theory developed in [4] and [5], necessary and sufficient conditions are derived for quaternionic projective spaces ℍPk and odd-dimensional complex projective spaces ℂP2k+1, of real dimension m say, to immerse in Euclidean space ℝ2m−1 in the range l ≦ 14. The results refine those obtained by Davis and Mahowald ([10, 11]) and earlier authors.

NECESSARY AND SUFFICIENT CONDITIONS FOR EXISTENCE OF A QUASIO-DOUBLE LINE OF A PAIR IN EUCLIDEAN SPACE

2021 ◽  
Vol 1 (1) ◽  
pp. 110-118
Author(s):  
Tolkun Mamataevna Papieva ◽  
Munavvarhon Khasanbaevna Abdulazizova ◽  
Baktygul Taalaibekovna Adieva ◽  
Eliza Muratbekovna Isakova ◽  
Baktygul Maksatbek kyzy
Keyword(s):  
Euclidean Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Double Line ◽  
Necessary And Sufficient

scholarly journals Darboux Iso-Geodesic Special Curve in Euclidean Space

2019 ◽  
Vol 13 (9) ◽  
pp. 98
Author(s):  
M. M. Wageeda ◽  
E. M. Solouma ◽  
M. Bary
Keyword(s):  
Euclidean Space ◽  
Linear Combination ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
The Family ◽  
Darboux Frame ◽  
Necessary And Sufficient ◽  
Special Curve

In this paper, by using Darboux frame we scrutinize the issues of reconstructing surfaces with given some unusual Smarandache curves in Euclidean 3-space, we make manifest the family of surfaces as a linear combination of the components of this frame and derive the necessary and sufficient conditions for coefficients to satisfy both the iso-geodesic and iso-parametric requirements.

scholarly journals Semi-parallel and harmonic surfaces in semi-Euclidean 4-space with index 2

Filomat ◽  
2019 ◽  
Vol 33 (17) ◽  
pp. 5743-5753
Author(s):  
Mehmet Yildirim ◽  
Kazim İlarslan
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Translation Surface ◽  
Translation Surfaces ◽  
Parallel Surfaces ◽  
Index 2 ◽  
Necessary And Sufficient

The present paper mainly deals with construction and investigation further properties of semi-parallel and harmonic surfaces. The first part of the study shall be devoted to investigate and present necessary and sufficient conditions of being semi-parallel surfaces by considering semi-parallelity condition R(X,Y).h = 0. In the light of the condition, the fact of a part of semi-parallel surfaces can be created by translation surfaces is captured. As a last result, we present that M must be a translation surface in the case of it is a harmonic surface.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

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