Abstract

The object of the present paper is to introduce the notion of generalized φ-recurrent Sasakian manifold and study its various geometric properties with the existence of such notion. Among others we study generalized concircularly φ-recurrent Sasakian manifolds. The existence of generalized φ-recurrent Sasakian manifold is given by a proper example.

Highlights

  • Let M be an n-dimensional connected Riemannian manifold with Riemannian metric g and Levi-Civita connection

  • The object of the present paper is to introduce the notion of generalized φ-recurrent Sasakian manifold and study its various geometric properties with the existence of such notion

  • Among others we study generalized concircularly φ-recurrent Sasakian manifolds

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Summary

Introduction

Let M be an n-dimensional connected Riemannian manifold with Riemannian metric g and Levi-Civita connection. By extending the notion of local φ-symmetry of Takahashi [7], De et al [8] introduced and studied the notion of φ-recurrent Sasakian manifold. The manifold M, n > 2, is called generalized recurrent [14] if its curvature tensor R of type (1,3) satisfies the condition. M, n > 2, is called generalized Ricci-recurrent manifold [16] if its Ricci tensor S of type (0, 2) satisfies the condition. The object of the present paper is to introduce a type of non-flat Sasakian manifolds called generalized φ-recurrent Sasakian manifold, which includes both the notion of local φ-symmetry of Takahashi [7] and φrecurrence of De et al [8] as particular cases.

Sasakian Manifolds
Generalized φ-Recurrent Sasakian Manifolds
Generalized Concircularly φ-Reccurent Sasakian Manifolds
A Y n n2 4n 5
Example of Generalized φ-Recurrent Sasakian Manifold
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