η-Ricci Soliton and Its Applications on φ-Recurrent LP Sasakian Manifold

The objective of this paper is to study the φ-recurrent nature and application of LP-Sasakian manifold associated with η̈ -Ricci soliton. Initially, we introduce an example to show the existance of LP Sasakian manifold equipped with η̈ -Ricci soliton. The idea of Ricci soliton recognized as a generalization of an Einstein metric and governing as the solution of partial differential equations representing Ricci flow. Some conditions have been obtained representing the nature of soliton (expanding, unchanged and shrinkingness) in pseudo projective, Weyl projective and semi generlized curvature with φ-recurrent condition. The application of η̈ -Ricci Soliton on spacetime also discussed.