SEMI‐RIEMANNIAN GEOMETRY With Applications to Relativity

We give an up-to-date overview of geometric and topological properties of cosymplectic and coKaehler manifolds. We also mention some of their applications to time-dependent mechanics.

A survey on cosymplectic geometry

In this paper, contact metric and trans-Sasakian generalized Sasakian-space-forms are deeply studied. We present some general results for manifolds with dimension greater than or equal to 5, and we also pay a special attention to the 3-dimensional cases.

Structures on generalized Sasakian-space-forms

We give an up-to-date overview of geometric and topological properties of cosymplectic and coKahler manifolds. We also mention some of their applications to time-dependent mechanics.

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a Survey on Cosymplectic Geometry

We show that, if a 3-dimensional Kenmotsu metric is a Ricci soliton then it is of constant curvature −1 and the soliton is expanding.

Kenmotsu 3-metric as a Ricci soliton

Generalized Sasakian-space-forms are introduced and studied. Many examples of these manifolds are presented, by using some different geometric techniques such as Riemannian submersions, warped products or conformal and related transformations. New results on generalized complex-space-forms are also obtained.

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Generalized Sasakian-space-forms

The study of generalized Sasakian space forms is continued in this paper. The behavior of such spaces under generalized D-conformal deformations is analyzed. As a consequence, new examples of generalized Sasakian space forms are given.

Generalized Sasakian Space Forms and Conformal Changes of the Metric

In the present paper submanifolds of generalized Sasakian-spaceforms are studied. We focus on almost semi-invariant submanifolds, these generalize invariant, anti-invariant, and slant submanifolds. Sectional curvatures, Ricci tensor and scalar curvature are also studied. The paper finishes with some results about totally umbilical submanifolds.

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Submanifolds of generalized sasakian space forms

In this paper we introduce the notion of slant submanifolds of a Lorentzian almost contact manifold and of a Lorentzian almost para contact mani- fold.

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Pablo Alegre

Papers

Generalized Sasakian-space-forms

Structures on generalized Sasakian-space-forms

Generalized Sasakian Space Forms and Conformal Changes of the Metric

Submanifolds of generalized sasakian space forms

Slant submanifolds of lorentzian sasakian and para sasakian manifolds