A New Class Of Pseudo Riemannian Algebraic Ricci Solitons

In this thesis,based on Lie group Lie algebras and their differential geometry,combined with the classification theorem of Ricci solitons in Riemannian solvable algebras,a general method for constructing a new class of pseudo-Riemannian solvable algebraic Ricci solitons is proposed,and at the same time we obtain the sufficient and necessary conditions for the isomorphism of pseudoRiemannian solvable algebraic Ricci solitons on solvable Lie groups.That is,for any δ∈Λ,<,>δ is a pseudo-Riemannian algebraic Ricci soliton on S.For different δ∈Λ andδ’∈Λ,<,>δ and<,>δ’are different from each other.The main contents are summarized as follows:(1)The first innovative point of this thesis is the construction of a new class of pseudoRiemannian solvable algebraic Ricci solitons,that is,for any δ∈Λ,<,>δ is a class of pseudoRiemannian algebraic Ricci soliton.(2)The second innovation point obtains sufficient necessary conditions for the isomorphism of pseudo-Riemang-solvable algebraic Ricci solitons on the solvable Lie group based on a new class of pseudo-Riemang solvable algebraic Ricci solitons constructed.That is,on the solvable lie group,the necessary condition for the isomorphism of any δ∈Λ,δ’∈Λ,<,>δ and<,>δ’is δ=δ’.(3)The third point of innovation is the necessary condition for solving the pseudo-Riemanic solvable algebraic Ricci solitons isomorphism on the solvable Lie group,That is,on the solvable lie group,the sufficient condition for the isomorphism of any δ∈Λ,δ’∈Λ<,>δ and<,>δ’is δ=δ’.