Generalized $${{(\kappa, \mu)}}$$ -Space Forms

Abstract

Abstract. Generalized (κ, µ)-space forms are introduced and studied. We examine in depth the contact metric case and present examples for all possible dimensions. We also analyse the trans-Sasakian case.

Some results on generalized (k, ?)-space forms

“…Let the φ -sectional curvature (3 f 2 + f 1 ) ( see [9]) of generalized (k, µ)-space form be constant. Then (23) gives…”

“…Generalized Sasakian space forms were studied extensively in [1,2,3,15,18,19,25]. An almost contact metric manifold (M, φ , ξ , η, g) is a generalized (k, µ) space form if there exists differential functions f 1 , f 2 , · · · , f 6 on M 2n+1 ( f 1 , · · · , f 6 ), whose curvature tensor R is given by [8,9]…”

On doubly warped product submanifolds of generalized $$(\kappa ,\mu )$$ ( κ , μ ) -space forms

“…In [4] A. Carriazo, V. Martín Molina and M. M. Tripathi introduce generalized (κ, µ)space forms as an almost contact metric manifold (M , φ, ξ, η, g) whose curvature tensor can be written as where f 1 , f 2 , f 3 , f 4 , f 5 , f 6 are differentiable functions onM , and R 1 , R 2 , R 3 , R 4 , R 5 , R 6 are the tensors defined by…”

“…[4]). We say that an almost contact metric manifold (M , φ, ξ, η, g) is a generalized (κ, µ)-space form if there exist functions f 1 , f 2 , f 3 , f 4 , f 5 , f 6 defined on M such that…”

On 3-Dimensional Contact Metric Generalized(k,μ)-Space Forms

“…By motivating the works on generalized Sasakian-spaceforms and ( , )-space forms, Carriazo et al [12] introduced the concept of generalized ( , )-space forms. A generalized ( , )-space form is an almost contact metric manifold ( , , , , ) whose curvature tensor is given by…”