Genelleştirilmiş 1-Tipinden Gauss Tasvirine Sahip Minkowski Uzayının Yarı-Riemann Alt Manifoldları

Year 2022, , 536 - 551, 30.06.2022

Burcu Bektaş Demirci

https://doi.org/10.35414/akufemubid.1109995

Abstract

Bu makalede, genelleştirilmiş 1-tipinden Gauss tasvirine sahip Minkowski uzayındaki dönel yüzeyler ve regle alt manifoldları üzerine çalışılmıştır. İlk olarak, ikinci çeşit noktasal 1-tipinden Gauss tasviri ile genelleştirilmiş 1-tipinden Gauss tasviri kavramları arasındaki ilişki verilmiştir. Daha sonra, 3-boyutlu Minkowski uzayında sabit ortalama eğriliğe sahip tümden jeodezik olmayan herhangi bir yüzeyin genelleştirilmiş 1-tipinden Gauss tasvirine sahip olamayacağı ispatlanmıştır. Diğer bölümde, E_1^3 uzayındaki bütün dönel yüzeylerin genelleştirilmiş 1-tipinden Gauss tasvirine sahip olduğu gösterilmiştir. Ayrıca, genelleştirilmiş 1-tipinden Gauss tasvirine sahip dönel yüzeylerle ilgili bir örnek verilmiştir. Son bölümde ise, E_1^(m )Minkowski uzayındaki regle alt manifoldları üzerine çalışılmıştır ve genelleştirilmiş 1-tipinden Gauss tasvirine sahip silindirik regle alt manifoldları incelenmiştir.

Keywords

Genelleştirilmiş 1-Tipinden GaussTasviri, Dönel Yüzeyler, Minkowski Uzayı, Regle Alt Manifoldları

Pseudo-Riemannian Submanifolds of Minkowski Space with Generalized 1-Type Gauss Map

Abstract

In this article, we study on rotational surfaces and regle submanifolds of the Minkowski space with generalized 1-type Gauss map. First of all, we give a relation between notions of pointwise 1-type Gauss map of the second kind and generalized 1-type Gauss map. Then, we prove that any non-totally geodesic surface in 3-dimensional Minkowski space with constant mean curvature does not have a generalized 1-type Gauss map. In other section, we show that all rotational surfaces in E_1^3 have generalized 1-type Gauss map. Furthermore, we give an example for the rotational surface having generalized 1-type Gauss map. In last section, we study the ruled submanifolds in the Minkowski space E_1^m and we examine the cylindrical ruled submanifolds having generalized 1-type Gauss map.

Keywords

Generalized 1-Type Gauss map;, Rotational Surfaces, Minkowski Space, Ruled Submanifolds

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