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Adara M. Blaga

Publications and source records attributed to Adara M. Blaga.

48 records · Page 3Linked to original sources
arXiv2018

Generalized metallic structures

We study the properties of a generalized metallic, a generalized product and a generalized complex structure induced on the generalized tangent bundle of $M$ by a metallic Riemannian structure $(J,g)$ on $M$, providing conditions for their integrability with respect to a suitable connection. Moreover, by using methods of generalized geometry, we lift $(J,g)$ to metallic Riemannian structures on the tangent and cotangent bundles of $M$, underlying the relations between them.

math.DG↗
arXiv2018

Warped product submanifolds in metallic Riemannian manifolds

In this paper, we study the existence of proper warped product submanifolds in metallic (or Golden) Riemannian manifolds and we discuss about semi-invariant, semi-slant and, respectively, hemi-slant warped product submanifolds in metallic and Golden Riemannian manifolds. Also, we provide some examples of warped product submanifolds in Euclidean spaces.

math.DG↗
arXiv2018

Hemi-slant submanifolds in metallic Riemannian manifolds

The aim of our paper is to focus on some properties of hemi-slant submanifolds in metallic (and Golden) Riemannian manifolds. We give some characterizations for submanifolds to be hemi-slant submanifolds in metallic (or Golden) Riemannian manifolds and we obtain integrability conditions for the distributions involved. Examples of hemi-slant submanifolds of metallic and Golden Riemannian manifolds are given.

math.DG↗
arXiv2018

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.

math.DG↗
arXiv2018

Remarks on almost $η$-Ricci solitons in $(\varepsilon)$-para Sasakian manifolds

We consider almost $η$-Ricci solitons in $(\varepsilon)$-para Sasakian manifolds satisfying certain curvature conditions. In the gradient case we give an estimation of the Ricci curvature tensor's norm and express the scalar curvature of the manifold in terms of the functions that define the soliton. We also prove that if the Ricci operator is Codazzi, then the gradient $η$-Ricci soliton is expanding if $M$ is spacelike or shrinking if $M$ is timelike.

math.DG↗
arXiv2018

Slant and semi-slant submanifolds in metallic Riemannian manifolds

The aim of our paper is to focus on some properties of slant and semi-slant submanifolds of metallic Riemannian manifolds. We give some characterizations for submanifolds to be slant or semi-slant submanifolds in metallic or Golden Riemannian manifolds and we obtain integrability conditions for the distributions involved in the semi-slant submanifolds of Riemannian manifolds endowed with metallic or Golden Riemannian structures. Examples of semi-slant submanifolds of the metallic and Golden Riemannian manifolds are given.

math.DG↗
arXiv2018

Submanifolds in metallic Riemannian manifolds

The aim of our paper is to focus on some properties of submanifolds in Riemannian manifolds endowed with endomorphisms that generalize the Golden Riemannian structure, named metallic Riemannian structures. We focus on the properties of the structure induced on submanifolds, named by us $Σ$-metallic Riemannian structures, especialy regarding the normality of this types of structure. Examples of structures induced on a sphere of codimension 1 by some metallic Riemannian structures defined on an Euclidean space are given.

math.DG↗
arXiv2017

$η$-Ricci solitons on para-Kenmotsu manifolds

In the context of paracontact geometry, $η$-Ricci solitons are considered on manifolds satisfying certain curvature conditions: $(ξ,\cdot)_{R}\cdot S=0$, $(ξ,\cdot)_{S}\cdot R=0$, $(ξ,\cdot)_{W_2}\cdot S=0$ and $(ξ,\cdot)_{S}\cdot W_2=0$. We prove that on a para-Kenmotsu manifold $(M,φ,ξ,η,g)$, the existence of an $η$-Ricci soliton implies that $(M,g)$ is quasi-Einstein and if the Ricci curvature satisfies $(ξ,\cdot)_{R}\cdot S=0$, then $(M,g)$ is Einstein. Conversely, we give a sufficient condition for the existence of an $η$-Ricci soliton on a para-Kenmotsu manifold.

math.DG↗
arXiv2014

Generalized almost paracontact structures

The notion of generalized almost paracontact structure on the generalized tangent bundle $TM\oplus T^*M$ is introduced and its properties are investigated. The case when the manifold $M$ carries an almost paracontact metric structure is also discussed. Conditions for its transformed under a $β$- or a $B$-field transformation to be also a generalized almost paracontact structure are given. Finally, the normality of a generalized almost paracontact structure is defined and a characterization of a normal generalized almost paracontact structure induced by an almost paracontact one is given.

math.DG↗
arXiv2013

The geometry of product conjugate connections

Properties of pairs of product conjugate connections are stated with a special view towards the integrability of the given almost product structure. We define the analogous in product geometry of the structural and the virtual tensors from the Hermitian geometry and express the product conjugate connections in terms of these tensors. Some examples from the geometry of a pair of complementary distributions are discussed and for this case the above structural and virtual tensors are expressed in terms of O'Neill-Gray tensor fields.

math.DG↗
arXiv2008

On Some Geometric Structures Associated to a k-Symplectic Manifold

A canonical connection is attached to any k-symplectic manifold. We study the properties of this connection and its geometric applications to k-symplectic manifolds. In particular we prove that, under some natural assumption, any ksymplectic manifold admits an Ehresmann connection, discussing some corollaries of this result, and we find vanishing theorems for characteristic classes on a k-symplectic manifold.

math.DG↗