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
C. Murathan
Publications and source records attributed to C. Murathan.
Anti-invariant Riemannian Submersions from Kenmotsu Manifolds onto Riemannian manifolds
The purpose of this paper is to study anti-invariant Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds. Several fundamental results in this respect are proved. The integrability of the distributions and the geometry of foliations are investigated. We proved that there do not exist (anti-invariant) Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds such that characteristic vector field {\xi} is a vertical vector field. We gave a method to get horizontally conformal submersion examples from warped product manifolds onto Riemannian manifolds. Furthermore, we presented an example of anti-invariant Riemannian submersions in the case where the characteristic vector field {\xi} is a horizontal vector field and an anti-invariant horizontally conformal submersion such that {\xi} is a vertical vector field.
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Almost {\alpha}-Paracosymplectic Manifolds
This paper is a complete study of almost {\alpha}-paracosmplectic manifolds. We characterize almost {\alpha}-paracosmplectic manifolds which have para Kaehler leaves. Main curvature identities which are fulfilled by any almost {\alpha}-paracosmplectic manifold are found. We also proved that {\xi} 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 {\alpha}-para-Kenmotsu manifolds satisfying a certain nullity condition. We show that this condition is invariant under D_{{\gamma},{\beta}}-homothetic deformation. Furthermore, we construct examples of almost {\alpha}-paracosmplectic manifolds satisfying generalized nullity conditions
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Slant Riemannian Submersions from Sasakian Manifolds
We introduce slant Riemannian submersions from Sasakian manifolds onto Riemannian manifolds. We survey main results of slant Riemannian submersions defined on Sasakian manifolds. We also give an example of such slant submersions.
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Anti-Invariant Riemannian Submersions from Sasakian Manifolds
We introduce anti-invariant Riemannian submersions from Sasakian manifolds onto Riemannian manifolds. We survey main results of anti-invariant Riemannian submersions defined on Sasakian manifolds. We investigate necessary and sufficient condition for an anti-invariant Riemannian submersion to be totally geodesic and harmonic. We give examples of anti-invariant submersions such that characteristic vector field ξ is vertical or horizontal.
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Anti-Invariant Riemannian Submersions from Cosymplectic Manifolds
We introduce anti-invariant Riemannian submersions from cosymplectic manifolds onto Riemannian manifolds. We survey main results of anti-invariant Riemannian submersions defined on cosymplectic manifolds. We investigate necessary and sufficient condition for an anti-invariant Riemannian submersion to be totally geodesic and harmonic. We give examples of anti-invariant submersions such that characteristic vector field ξ is vertical or horizontal. Moreover we give decomposition theorems by using the existence of anti-invariant Riemannian submersions.
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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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