Immersion Of R-h-almost Newton-Yamabe Solitons Into Pseudo-Riemannian Manifolds

In this paper,we mainly study the spacelike r-h-almost Newton-Yamabe solitons Σn isometric immersed in pseudo-Riemannian manifolds Lqn+q.Under the appropriate assumptions of potential functions and soliton functions,the sufficient conditions for Σn to be totally geodesic,or totally umbilical,or trivial soliton are obtained by using the basic formulas and equations of the submanifolds of pseudoRiemannian manifolds.The main results of include the following three parts:First of all,on the premise that the second fundamental form of Σn is bounded,or that the Newton transformation Pr is above bounded in the sense of quadratic form,and the potential functions satisfies certain integrability conditions.Assuming the sectional curvature of the Lqn+q and the soliton functions satisfy some conditions,the paper obtains the sufficient conditions for Σn is not a minimal submanifolds,and further obtains the sufficient conditions for its totally geodesic or totally umbilical.Secondly,study is immersed in a locally symmetric pseudo-Riemannian manifolds Lqn+q that satisfies the curvature condition K(η,v)=-c1/n complete spacelike 1-h-almost Newton-Yamabe solitons Σn,using the ideas and methods of the first part,the paper proves the sufficient conditions for Σn is not a minimal submanifolds.In addition,it is obtained that Σn is a sufficient condition for totally geodesic submanifolds or totally umbilical submanifolds.Finally,a sufficient condition for Σn to be trivial r-h-almost Newton-Yamabe solitons is obtained by making appropriate assumptions on the scalar curvature of the Σn and the Newton transformation Pr.