Abstract
We prove a classification theorem of the generalized Sasakian space forms which are realized as real hypersurfaces in complex space forms.
Highlights
We prove a classification theorem of the generalized Sasakian space forms which are realized as real hypersurfaces in complex space forms
Alegre, Blair and Carriazo introduced [6] the generalized Sasakian space forms, which are almost contact metric manifolds whose curvature tensor generalizes the expression of the curvature tensor of Sasakian space forms
It is very interesting to give a classification of the generalized Sasakian space forms which are realized as real hypersurfaces in complex space forms
Summary
We include some definitions and results on almost contact metric geometry (for more details, see [7]). An almost contact metric manifold is called normal if [φ, φ]( X, Y ) = −dη ( X, Y )ξ, for any vector fields X, Y on M, where [φ, φ] is the Nijenhuis torsion of φ. Sasakian manifolds with constant φ-sectional curvature F are called Sasakian space forms and they are the analog on contact metric geometry to complex space forms in complex geometry. Generalized Sasakian space forms were introduced by Alegre, Blair and Carriazo [6] as almost contact metric manifolds M whose curvature tensor R can be written as. On a generalized Sasakian space form M2n−1 ( f 1 , f 2 , f 3 ), given a unit vector field X, orthogonal to ξ, the φ-sectional curvature K ( X, φX ) = g( R( X, φX )φX, X ) is independent of the direction X, since. The Ricci operator S as where I denotes the identity
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