349 research outputs found
Generalized metallic pseudo-Riemannian structures
We generalize the notion of metallic structure in the pseudo-Riemannian
setting, define the metallic Norden structure and study its integrability. We
construct a metallic natural connection recovering as particular case the
Ganchev and Mihova connection, which we extend to a metallic natural connection
on the generalized tangent bundle. Moreover, we construct metallic
pseudo-Riemannian structures on the tangent and cotangent bundles.Comment: 16 page
Generalized quasi-statistical structures
Given a non-degenerate -tensor field on a smooth manifold , we
consider a natural generalized complex and a generalized product structure on
the generalized tangent bundle of and we show that they are
-integrable, for an affine connection on , if and only if
is a quasi-statistical manifold. We introduce the notion of
generalized quasi-statistical structure and we prove that any quasi-statistical
structure on induces generalized quasi-statistical structures on . In this context, dual connections are considered and some of their
properties are established. The results are described in terms of
Patterson-Walker and Sasaki metrics on , horizontal lift and Sasaki
metrics on and, when the connection is flat, we define
prolongation of quasi-statistical structures on manifolds to their cotangent
and tangent bundles via generalized geometry. Moreover, Norden and Para-Norden
structures are defined on and .Comment: 28 page
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
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
-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
Invariant, anti-invariant and slant submanifolds of a metallic Riemannian manifold
Properties of invariant, anti-invariant and slant isometrically immersed
submanifolds of metallic Riemannian manifolds are given with a special view
towards the induced -structure. Examples of such metallic manifolds are
also given.Comment: 26 page
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.Comment: 10 page
Geometric solitons in a -homothetically deformed Kenmotsu manifold
We consider almost Riemann and almost Ricci solitons in a -homothetically
deformed Kenmotsu manifold having as potential vector field a gradient vector
field, a solenoidal vector field or the Reeb vector field of the deformed
structure, and explicitly obtain the Ricci and scalar curvatures for some
cases. We also provide a lower bound for the Ricci curvature of the initial
Kenmotsu manifold when the deformed manifold admits a gradient almost Riemann
or almost Ricci soliton
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