A Ricci soliton (M, g, v, λ) on a Riemannian manifold (M, g) is said to have concurrent potential field if its potential field v is a concurrent vector field. In the first part of this paper we classify Ricci solitons with concurrent potential fields. In the second part we derive a necessary and sufficient condition for a submanifold to be a Ricci soliton in a Riemannian manifold equipped with ...

in this paper, a useful classification of all lie subalgebras of a given lie algebraup to an inner automorphism is presented. this method can be regarded as animportant connection between differential geometry and algebra and has many applications in different fields of mathematics. after main results, we have applied this procedure for classifying the lie subalgebras of some examples of lie al...

Let $M$ is a (pseudo-)Riemannian manifold and $TM$ be its tangent bundlewith the semi-symmetric metric connection $\overline{\nabla }$. In thispaper, we examine some special vector fields, such as incompressible vectorfields, harmonic concurrent conformal vectorfields projective fields on with respect to thesemi-symmetric }$ obtain someproperties related them.

‎We consider the oscillator group equipped with‎ ‎a biinvariant Lorentzian metric‎. ‎Some geometrical properties of this space and the harmonicity properties of left-invariant vector fields on this space are determined‎. ‎In some cases‎, ‎all these vector fields are critical points for the energy functional‎ ‎restricted to vector fields‎. ‎Left-invariant vector fields defining harmonic maps are...

‎We consider four-dimensional lie groups equipped with‎ ‎left-invariant Lorentzian Einstein metrics‎, ‎and determine the harmonicity properties ‎of vector fields on these spaces‎. ‎In some cases‎, ‎all these vector fields are critical points for the energy functional ‎restricted to vector fields‎. ‎We also classify vector fields defining harmonic maps‎, ‎and calculate explicitly the energy of t...

This paper mainly devotes to the study of some solitons such as Ricci and Yamabe also their combination called Ricci-Yamabe solitons. In geometry solitons, a fundamental question is identify conditions under which these can be trivial. Firstly, in this we extensive results on generic contact CR-submanifolds Sasakian manifolds endowed with concurrent vector fields. Then applications submanifolds...

Recently, we have used the symmetric bracket of vector fields, and developed the notion of the symmetric derivation. Using this machinery, we have defined the concept of symmetric curvature. This concept is natural and is related to the notions divergence and Laplacian of vector fields. This concept is also related to the derivations on the algebra of symmetric forms which has been discu...

recently, we have used the symmetric bracket of vector fields, and developed the notion of the symmetric derivation. using this machinery, we have defined the concept of symmetric curvature. this concept is natural and is related to the notions divergence and laplacian of vector fields. this concept is also related to the derivations on the algebra of symmetric forms which has been discus...

We obtain some properties of a hyperbolic Ricci soliton with certain types potential vector fields, and we point out conditions when it reduces to trivial soliton. also study those submanifolds whose fields are the tangential components concurrent field on ambient manifold, in particular, show that totally umbilical is an Einstein manifold. prove if hypersurface Riemannian manifold constant cur...