A Generalized Wintgen inequality for Legendrian submanifolds in almost Kenmotsu manifolds
Main interest of the present paper is to obtain the generalized Wintgen inequality for Legendrian submanifolds in almost Kenmotsu manifolds.
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arXiv subjects
I. Kupeli Erken
Publications and source records attributed to I. Kupeli Erken.
Almost α-Paracosymplectic Manifolds
This paper is a complete study of almost α-paracosmplectic manifolds. We characterize almost α-paracosmplectic manifolds which have para Kaehler leaves. Main curvature identities which are fulfilled by any almost α-paracosmplectic manifold are found. We also proved that ξ is a harmonic vector field if and only if it is an eigen vector field of the Ricci operator. We locally classify three dimensional almost α-para-Kenmotsu manifolds satisfying a certain nullity condition. We show that this condition is invariant under D_{γ,β}-homothetic deformation. Furthermore, we construct examples of almost α-paracosmplectic manifolds satisfying generalized nullity conditions
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Nullity conditions in paracontact geometry
The paper is a complete study of paracontact metric manifolds for which the Reeb vector field of the underlying contact structure satisfies a nullity condition (the condition \eqref{paranullity} below, for some real numbers $% \tildeκ$ and $\tildeμ$). This class of pseudo-Riemannian manifolds, which includes para-Sasakian manifolds, was recently defined in \cite{MOTE}. In this paper we show in fact that there is a kind of duality between those manifolds and contact metric $(κ,μ)$-spaces. In particular, we prove that, under some natural assumption, any such paracontact metric manifold admits a compatible contact metric $(κ,μ)$-structure (eventually Sasakian). Moreover, we prove that the nullity condition is invariant under $% \mathcal{D}$-homothetic deformations and determines the whole curvature tensor field completely. Finally non-trivial examples in any dimension are presented and the many differences with the contact metric case, due to the non-positive definiteness of the metric, are discussed.
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