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Articles 1 - 9 of 9
Full-Text Articles in Physical Sciences and Mathematics
Clairaut Riemannian Maps, Kiran Meena, Akhilesh Yadav
Clairaut Riemannian Maps, Kiran Meena, Akhilesh Yadav
Turkish Journal of Mathematics
In this paper, first we define Clairaut Riemannian map between Riemannian manifolds by using a geodesic curve on the base space and find necessary and sufficient conditions for a Riemannian map to be Clairaut with a nontrivial example. We also obtain necessary and sufficient condition for a Clairaut Riemannian map to be harmonic. Thereafter, we study Clairaut Riemannian map from Riemannian manifold to Ricci soliton with a nontrivial example. We obtain scalar curvatures of $rangeF_\ast$ and $(rangeF_\ast)^\bot$ by using Ricci soliton. Further, we obtain necessary conditions for the leaves of $rangeF_\ast$ to be almost Ricci soliton and Einstein. We also …
Clairaut Invariant Riemannian Maps With Kahler Structure, Akhilesh Yadav, Kiran Meena
Clairaut Invariant Riemannian Maps With Kahler Structure, Akhilesh Yadav, Kiran Meena
Turkish Journal of Mathematics
In this paper, we study Clairaut invariant Riemannian maps from Kahler manifolds to Riemannian manifolds, and from Riemannian manifolds to Kahler manifolds. We find necessary and sufficient conditions for the curves on the total spaces and base spaces of invariant Riemannian maps to be geodesic. Further, we obtain necessary and sufficient conditions for invariant Riemannian maps from Kahler manifolds to Riemannian manifolds to be Clairaut invariant Riemannian maps. Moreover, we obtain a necessary and sufficient condition for invariant Riemannian maps from Riemannian manifolds to Kahler manifolds to be Clairaut invariant Riemannian maps. We also give nontrivial examples of Clairaut invariant …
Some Recent Results In Plastic Structure On Riemannian Manifold, Akbar Dehghan Nezhad, Zohreh Aral
Some Recent Results In Plastic Structure On Riemannian Manifold, Akbar Dehghan Nezhad, Zohreh Aral
Turkish Journal of Mathematics
The plastic ratio is a fascinating topic that continually generates new ideas. The purpose of this paper is to point out and find some applications of the plastic ratio in the differential manifold. Precisely, we say that an $(1,1)$-tensor field $P$ on a $m$-dimensional Riemannian manifold $(M, g)$ is a plastic structure if it satisfies the equation $ P^3 = P + I $, where $ I $ is the identity. We establish several properties of the plastic structure. Then we show that a plastic structure induces on every invariant submanifold a plastic structure, too.
On 3-Dimensional Almost Einstein Manifolds With Circulant Structures, Iva Dokuzova
On 3-Dimensional Almost Einstein Manifolds With Circulant Structures, Iva Dokuzova
Turkish Journal of Mathematics
A 3-dimensional Riemannian manifold equipped with a tensor structure of type (1,1), whose third power is the identity, is considered. This structure and the metric have circulant matrices with respect to some basis, i.e. these structures are circulant. An associated manifold, whose metric is expressed by both structures, is studied. Three classes of such manifolds are considered. Two of them are determined by special properties of the curvature tensor of the manifold. The third class is composed by manifolds whose structure is parallel with respect to the Levi-Civitaconnection of the metric. Some geometric characteristics of these manifolds are obtained. Examples …
Riemannian Manifolds Admitting A New Type Of Semisymmetric Nonmetric Connection, Sudhakar K. Chaubey, Ahmet Yildiz
Riemannian Manifolds Admitting A New Type Of Semisymmetric Nonmetric Connection, Sudhakar K. Chaubey, Ahmet Yildiz
Turkish Journal of Mathematics
We define a new type of semisymmetric nonmetric connection on a Riemannian manifold and establish its existence. It is proved that such connection on a Riemannian manifold is projectively invariant under certain conditions. We also find many basic results of the Riemannian manifolds and study the properties of group manifolds and submanifolds of the Riemannian manifolds with respect to the semisymmetric nonmetric connection. To validate our findings, we construct a nontrivial example of a $3$-dimensional Riemannian manifold equipped with a semisymmetric nonmetric connection.
On Metallic Riemannian Structures, Aydin Gezer, Çağri Karaman
On Metallic Riemannian Structures, Aydin Gezer, Çağri Karaman
Turkish Journal of Mathematics
The paper is devoted to the study of metallic Riemannian structures. An integrability condition and curvature properties for these structures by means of a $\Phi $-operator applied to pure tensor fields are presented. Examples of these structures are also given.
Relaxed Elastic Line In A Riemannian Manifold, Gözde Özkan, Ahmet Yücesan
Relaxed Elastic Line In A Riemannian Manifold, Gözde Özkan, Ahmet Yücesan
Turkish Journal of Mathematics
We obtain a differential equation with 2 boundary conditions for a relaxed elastic line in a Riemannian manifold. This differential equation, which is found with respect to constant sectional curvature G, geodesic curvature \kappa, and 2 boundary conditions, gives a more direct and more geometric approach to questions concerning a relaxed elastic line in a Riemannian manifold. We give various theorems and results in terms of a relaxed elastic line. Consequently, we examine the concept of a relaxed elastic line in 2- and 3- dimensional space forms.
On Integrability Of Golden Riemannian Structures, Aydin Gezer, Nejmi̇ Cengi̇z, Arif Salimov
On Integrability Of Golden Riemannian Structures, Aydin Gezer, Nejmi̇ Cengi̇z, Arif Salimov
Turkish Journal of Mathematics
The main purpose of the present paper is to study the geometry of Riemannian manifolds endowed with Golden structures. We discuss the problem of integrability for Golden Riemannian structures by using a \phi-operator which is applied to pure tensor fields. Also, the curvature properties for Golden Riemannian metrics and some properties of twin Golden Riemannian metrics are investigated. Finally, some examples are presented.
Applications Of The Golden Ratio On Riemannian Manifolds, Cristina-Elena Hretcanu, Mircea Craşmareanu
Applications Of The Golden Ratio On Riemannian Manifolds, Cristina-Elena Hretcanu, Mircea Craşmareanu
Turkish Journal of Mathematics
The Golden Ratio is a fascinating topic that continually generates new ideas. The main purpose of the present paper is to point out and find some applications of the Golden Ratio and of Fibonacci numbers in Differential Geometry. We study a structure defined on a class of Riemannian manifolds, called by us a Golden Structure. A Riemannian manifold endowed with a Golden Structure will be called a Golden Riemannian manifold. Precisely, we say that an (1,1)-tensor field \widetilde{P} on a m-dimensional Riemannian manifold (\widetilde{M}, \widetilde{g}) is a Golden Structure if it satisfies the equation \widetilde{P}^{2}=\widetilde{P}+I (which is similar to that …