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A new class of almost complex structures on tangent bundle of a Riemannian manifold

Amir Baghban; Esmaeil Abedi — 2018

Communications in Mathematics

In this paper, the standard almost complex structure on the tangent bunle of a Riemannian manifold will be generalized. We will generalize the standard one to the new ones such that the induced $(0, 2)$ -tensor on the tangent bundle using these structures and Liouville $1$ -form will be a Riemannian metric. Moreover, under the integrability condition, the curvature operator of the base manifold will be classified.

Isotropic almost complex structures and harmonic unit vector fields

Amir Baghban; Esmaeil Abedi — 2018

Archivum Mathematicum

Isotropic almost complex structures $J_{δ, σ}$ define a class of Riemannian metrics $g_{δ, σ}$ on tangent bundles of Riemannian manifolds which are a generalization of the Sasaki metric. In this paper, some results will be obtained on the integrability of these almost complex structures and the notion of a harmonic unit vector field will be introduced with respect to the metrics $g_{δ, 0}$ . Furthermore, the necessary and sufficient conditions for a unit vector field to be a harmonic unit vector field will be obtained.

Ricci and scalar curvatures of submanifolds of a conformal Sasakian space form

Esmaeil Abedi; Reyhane Bahrami Ziabari; Mukut Mani Tripathi — 2016

Archivum Mathematicum

We introduce a conformal Sasakian manifold and we find the inequality involving Ricci curvature and the squared mean curvature for semi-invariant, almost semi-invariant, $θ$ -slant, invariant and anti-invariant submanifolds tangent to the Reeb vector field and the equality cases are also discussed. Also the inequality involving scalar curvature and the squared mean curvature of some submanifolds of a conformal Sasakian space form are obtained.

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Currently displaying 1 – 3 of 3

A new class of almost complex structures on tangent bundle of a Riemannian manifold

Isotropic almost complex structures and harmonic unit vector fields

Ricci and scalar curvatures of submanifolds of a conformal Sasakian space form