Pseudo-spherical submanifolds with 1-type pseudo-spherical Gauss map

In this work, we study the pseudo-Riemannian submanifolds of a pseudo-sphere with 1-type pseudo-spherical Gauss map. First, we classify the Lorentzian surfaces in a 4-dimensional pseudo-sphere $\mathbb{S}^4_s(1)$ with index s, $s=1, 2$, and having harmonic pseudo-spherical Gauss map. Then we give a characterization theorem for pseudo-Riemannian submanifolds of a pseudo-sphere $\mathbb{S}^{m-1}_s(1)\subset\mathbb{E}^m_s$ with 1-type pseudo-spherical Gauss map, and we classify spacelike surfaces and Lorentzian surfaces in the de Sitter space $\mathbb{S}^4_1(1)\subset\mathbb{E}^5_1$ with 1-type pseudo-spherical Gauss map. Finally, according to the causal character of the mean curvature vector we obtain the classification of submanifolds of a pseudo-sphere having 1-type pseudo-spherical Gauss map with nonzero constant component in its spectral decomposition

QUASI-RECURRENT WEYL SPACES

In this work we define Quasi-Recurrent Weyl spaces and examine the hypersurfaces of them

Classification of surfaces in a pseudo-sphere with 2-type pseudo-spherical Gauss map

In this article, we study submanifolds in a pseudo-sphere with 2-type pseudo-spherical Gauss map. We give a characterization theorem for Lorentzian surfaces in the pseudosphere S-2(4) subset of E-2(5) with zero mean curvature vector in S-2(4) and 2-type pseudo-spherical Gauss map. We also prove that non-totally umbilical proper pseudo-Riemannian hypersurfaces in a pseudo-sphere S-s(n+1) subset of E-s(n+2) with non-zero constant mean curvature has 2-type pseudo-spherical Gauss map if and only if it has constant scalar curvature. Then, for n = 2 we obtain the classification of surfaces in S-1(3) subset of E-1(4) with 2-type pseudo-spherical Gauss map. Finally, we give an example of surface with null 2-type pseudo-spherical Gauss map which does not appear in Riemannian case, andwe give a characterization theorem for Lorentzian surfaces in S-1(3) subset of E-1(4) with null 2-type pseudospherical Gauss map.Publisher's Versio

On pseudo-umbilical rotational surfaces with pointwise 1-type gauss map in E-2(4)

In this work, we study two families of rotational surfaces in the pseudo Euclidean space 1E4 with profile curves lying in 2 dimensional planes. First, we obtain a classification of pseudo umbilical spacelike surfaces and timelike surfaces in these families. Then, we show that in this classification there exists no a pseudo umbilical rotational surface in 1E4 with pointwise 1 type Gauss map of second kind. Finally, we determine such pseudo umbilical rotational surfaces in 1E4 having pointwise 1 type Gauss map of first kind.Publisher's VersionWOS:00061325320000

On Caputo fractional Bertrand curves in E3 and E31

In this article, we examine Bertrand curves in E3 and E31 by using the Caputo fractional derivative which we call alpha-Bertrand Curves. First, we consider alpha-Bertrand curves in E3 and we give a characterization of them. Then, we study alpha-Bertrand curves in E31 and we prove the necessary and sufficient condition for a alpha-Bertrand curves in E31 by considering time like, space like and null curves. We also give the related examples by using Python.Publisher's VersionQ3WOS:00112659690000

Pseudo-spherical submanifolds with 1-type pseudo-spherical gauss map

In this work, we study pseudo-Riemannian submanifolds of a pseudo-sphere with 1-type pseudo-spherical Gauss map. First, we classify Lorentzian surfaces in a 4-dimensional pseudo-sphere (Formula presented.) with index s, (Formula presented.), and having harmonic pseudo-spherical Gauss map. Then we give a characterization theorem for pseudo-Riemannian submanifolds of a pseudo-sphere (Formula presented.) with 1-type pseudo-spherical Gauss map, and we classify spacelike surfaces and Lorentzian surfaces in the de Sitter space (Formula presented.) with 1-type pseudo-spherical Gauss map. Finally, according to the causal character of the mean curvature vector we obtain the classification of submanifolds of a pseudo-sphere having 1-type pseudo-spherical Gauss map with nonzero constant component in its spectral decomposition.Publisher's Versio

On quasi-recurrent spaces with Ricci quarter-symmetric metric connection

Uysal, Samiye Aynur (Dogus Author)In [3], Mishra and Pandey defined Ricci quarter-symmetric metric connection in Riemanian manifold. In [5],Uysal and Doğan defined D-recurrent spaces with semi-symmetric metric connection and constructed an example of these spaces. In these paper we define quasirecurrent spaces with Ricci quarter- symmetric metric connection and establish an example of such spaces