CONFORMAL AND PARACONTACTLY GEODESIC TRANSFORMATIONS OF ALMOST PARACONTACT METRIC STRUCTURES

We give the expressions of the virtual and the structure tensor fields of an almost paracontact metric structure. We also introducethe notion of paracontactly geodesic transformation and prove thatthe structure tensor field is invariant under conformal andparacontactly geodesic transformations. For the particular case of para-Kenmotsu structure, we give a necessary and sufficient condition for a conformal transformation to map it to an $\alpha$-para-Kenmotsu structure and show that a para-Kenmotsu manifold admits no nontrivial paracontactly geodesic transformation of the metric. In the conformal case, the virtual tensor field is invariant. 

REMARKS ON SUBMANIFOLDS AS ALMOST eta-RICCI-BOURGUIGNON SOLITONS

We give some characterizations for submanifolds admitting almost $\eta$-Ricci-Bourguignon solitons whose potential vector field is the tangential component of a concurrent vector field on the ambient manifold. We describe the particular cases of umbilical submanifolds and of hypersurfaces in a space with constant curvature

INEQUALITIES FOR GRADIENT EINSTEIN AND RICCI SOLITONS

This short note concerns with two inequalities in the geo\-me\-try of gradient Einstein solitons $(g, f, \lambda )$ on a smooth manifold $M$. These inequalities provide some relationships between the curvature of the Riemannian metric $g$ and the behavior of the scalar field $f$ through two quadratic equations satisfied by the scalar $\lambda$. The similarity with gradient Ricci solitons and a slightly generalization involving a $g$-symmetric endomorphism $A$ are provided

SOME REMARKS ON RICCI{GOLAB CONNECTIONS

We consider the divergence and Laplace operators defned by the Ricci-Golab connection and establish some integral properties. We provide certain results on the deformation algebras associated to pairs of Ricci-Golab connections. Almost 1-principal Golab connections are also investigated

Remarks on metallic warped product manifolds

We characterize the metallic structure on the product of two metallic manifolds in terms of metallic maps and provide a necessary and sufficient condition for the warped product of two locally metallic Riemannian manifolds to be locally metallic. The particular case of product manifolds is discussed and an example of metallic warped product Riemannian manifold is provided

η-Ricci solitons in (ε)-almost paracontact metric manifolds

The object of this paper is to study η -Ricci solitons on ( ε ) -almost paracontact metric manifolds. We investigate η -Ricci solitons in the case when its potential vector field is exactly the characteristic vector field ξ of the ( ε ) -almost paracontact metric manifold and when the potential vector field is torse-forming. We also study Einstein-like and ( ε )-para Sasakian manifolds admitting η-Ricci solitons. Finally we obtain some results for η -Ricci solitons on ( ε )-almost paracontact metric manifolds with a special view towards parallel symmetric (0,2) -tensor fields

Screen transversal lightlike submanifolds of metallic semi-Riemannian manifolds

WOS: 000472701500008In the present paper, we introduce screen transversal lightlike submanifolds of metallic semi-Riemannian manifolds with its subclasses, namely screen transversal anti-invariant, radical screen transversal and isotropic screen transversal lightlike submanifolds, and give an example. We show that there do not exist co-isotropic and totally screen transversal type of screen transversal anti-invariant lightlike submanifolds of a metallic semi-Riemannian manifold. We investigate the geometry of distributions involved in the definition of such submanifolds and the conditions for the induced connection to be a metric connection. Furthermore, we give a necessary and sufficient condition for an isotropic screen transversal lightlike submanifold to be totally geodesic. (C) 2019 Elsevier B.V. All rights reserved