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Hristo Manev

Publications and source records attributed to Hristo Manev.

At least 19 recordsLinked to original sources
arXiv2023

Second natural connection on Riemannian $Π$-manifolds

A natural connection, determined by a property of its torsion tensor, is defined and it is called the second natural connection on Riemannian $Π$-manifold, i.e. the uniqueness of this connection is proved and a necessary and sufficient condition for coincidence with the first natural connection on the considered manifolds is found. The form of the torsion tensor of the second natural connection is obtained in the classes of the Riemannian $Π$-manifolds in which it differs from the first natural connection. An explicit example of dimension 5 is given in support of the proven assertions.

math.DG↗
arXiv2023

First natural connection on Riemannian $Π$-manifolds

A natural connection with torsion is defined and it is called the first natural connection on Riemannian $Π$-manifold. Relations between the introduced connection and the Levi-Civita connection are obtained, as well as relations between their respective curvature tensors, torsion tensors, Ricci tensors, and scalar curvatures in the main classes of a classification of Riemannian $Π$-manifolds are presented. An explicit example of dimension 5 is provided.

math.DG↗
arXiv2022

Para-Ricci-like solitons with arbitrary potential on para-Sasaki-like Riemannian $Π$-manifolds

Para-Ricci-like solitons with arbitrary potential on para-Sasaki-like Riemannian $Π$-manifolds are introduced and studied. For the studied soliton, it is proved that its Ricci tensor is a constant multiple of the vertical component of both metrics. Thus, the corresponding scalar curvatures of both considered metrics are equal and constant. An explicit example of the Lie group as the manifold under study is presented.

math.DG↗
arXiv2022

Gradient almost para-Ricci-like solitons on para-Sasaki-like Riemannian $Π$-manifolds

Gradient almost para-Ricci-like solitons on para-Sasaki-like Riemannian $Π$-manifolds are studied. It is proved that these objects have constant soliton coefficients. For the soliton under study is shown that the corresponding scalar curvatures of the considered both metrics are equal and constant and its Ricci tensor is a constant multiple of the vertical component. Explicit example of a 3-dimensional para-Sasaki-like Riemannian $Π$-manifold is provided in support of the proved assertions.

math.DG↗
arXiv2021

Para-Ricci-like Solitons with Vertical Potential on Para-Sasaki-Like Riemannian $Π$-Manifolds

Object of study are para-Ricci-like solitons on para-Sasaki-like almost paracontact almost paracomplex Riemannian manifolds, briefly, Riemannian $Π$-manifolds. Different cases when the potential of the soliton is the Reeb vector field or pointwise collinear to it are considered. Some additional geometric properties of the constructed objects are proven. Results for a parallel symmetric second-order covariant tensor on the considered manifolds are obtained. Explicit example of dimension 5 in support of the given assertions is provided.

math.DG↗
arXiv2021

Para-Ricci-like Solitons on Almost Paracontact Almost Paracomplex Riemannian Manifolds

It is introduced and studied para-Ricci-like solitons with potential Reeb vector field on almost paracontact almost paracomplex Riemannian manifolds. The special cases of para-Einstein-like, para-Sasaki-like and having a torse-forming Reeb vector field have been considered. It is proved a necessary and sufficient condition the manifold to admit a para-Ricci-like soliton which is the structure to be para-Einstein-like. Explicit examples are provided in support of the proven statements.

math.GM↗
arXiv2021

Lie groups of dimension 4 and almost hypercomplex manifolds with Hermitian-Norden metrics

Object of investigation are almost hypercomplex manifolds with Hermitian-Norden metrics of the lowest dimension. The considered manifolds are constructed on 4-dimensional Lie groups. It is established a relation between the classes of a classification of 4-dimensional indecomposable real Lie algebras and the classification of the manifolds under study. The basic geometrical characteristics of the constructed manifolds are studied in the frame of the mentioned classification of the Lie algebras.

math.DG↗
arXiv2020

Pair of associated Schouten-van Kampen connections adapted to an almost paracontact almost paracomplex Riemannian structure

There are introduced and studied a pair of associated Schouten-van Kampen affine connections adapted to the paracontact distribution and an almost paracontact almost paracomplex Riemannian structure generated by the pair of associated metrics and their Levi-Civita connections. By means of the constructed non-symmetric connections, the basic classes of the manifolds with the considered structure are characterized. Curvature properties of the studied connections are obtained. A family of examples on a Lie group is constructed.

math.DG↗
arXiv2020

Para-Sasaki-like Riemannian manifolds and new Einstein metrics

We extract a new class of paracontact paracomplex Riemannian manifolds arising from certain cone construction, call it para-Sasaki-like Riemannian manifold and give explicit examples. We define a hyperbolic extension of a paraholomorphic paracomplex Riemannian manifold, which is a local product of two Riemannian spaces with equal dimensions, showing that it is a para-Sasaki-like Riemannian manifold. If the starting paraholomorphic paracomplex Riemannian manifold is complete Einstein with negative scalar curvature then its hyperbolic extension is a complete Einstein para-Sasaki-like Riemannian manifold with negative scalar curvature thus producing new examples of complete Einstein Riemannian manifold with negative scalar curvature.

math.DG↗
arXiv2019

Almost hypercomplex manifolds with Hermitian-Norden metrics and 4-dimensional indecomposable real Lie algebras depending on two parameters

The object of investigations are almost hypercomplex structures with Hermitian-Norden metrics on 4-dimensional Lie groups considered as smooth manifolds. There are studied both the basic classes of a classification of 4-dimensional indecomposable real Lie algebras depending on two parameters. Some geometric characteristics of the respective almost hypercomplex manifolds with Hermitian-Norden metrics are obtained.

math.DG↗
arXiv2019

Matrix Lie Groups as 4-Dimensional Hypercomplex Manifolds with Hermitian-Norden metrics

There are studied Lie groups considered as almost hypercomplex Hermitian-Norden manifolds, which are integrable and have the lowest dimension four. It is established a correspondence of the derived Lie algebras of types of invariant hypercomplex structures and the explicit matrix representation of their Lie groups. There are constructed examples of the considered structure of different types on some known Lie groups.

math.DG↗
arXiv2017

Design, analysis and implementation of electronic test for knowledge evaluation in the course of Information Technologies for pharmaceutical students

The increased usage of the information technologies in everyday life and especially in education leads to demands for new forms of teaching, studying and appropriate examination and evaluation of acquired knowledge and skills of the students. Modern electronic educational systems use only those technologies that improve the learning process and make it more effective. The interactive education provides an opportunity to develop skills for independent literature research and activation of the cognitive activity. In this work, it is shown how a modern electronic education is implemented in the curriculum of English language pharmaceutical students at the Medical University - Plovdiv in the course of Information Technologies. It is developed a methodological approach of a hybrid system, i.e. a compulsory attendance at lectures in combination with two different types of conduction of the final test for comparison - a paper-based test and a remote web-based one. The results received from the parallel tests are processed and analysed and the conclusions are used to enhance the quality of the developed test and the type of implementation. Moreover, the examined students fill in an anonymous poll to show the authors their thoughts for this type of hybrid educational system.

cs.CY↗
arXiv2016

Holomorphic submanifolds of some hypercomplex manifolds with Hermitian and Norden metrics

In this paper we initiate the study of submanifolds of almost hypercomplex manifolds with Hermitian and Norden metrics. Object of investigations are holomorphic submanifolds of the hypercomplex manifolds which are locally conformally equivalent to the hyper-Kähler manifolds of the considered type. Necessary and sufficient conditions the investigated holomorphic submanifolds to be totally umbilical or totally geodesic are obtained. Examples of the examined submanifolds are constructed.

math.DG↗
arXiv2015

Slant null curves on normal almost contact B-metric 3-manifolds with parallel Reeb vector field

In this paper we study slant null curves with respect to the original parameter on 3-dimensional normal almost contact B-metric manifolds with parallel Reeb vector field. We prove that for non-geodesic such curves there exists a unique Frenet frame for which the original parameter is distinguished. Moreover, we obtain a necessary condition this Frenet frame to be a Cartan Frenet frame with respect to the original parameter. Examples of the considered curves are constructed.

math.DG↗
arXiv2015

Almost contact B-metric manifolds as extensions of a 2-dimensional space-form

The object of investigations are almost contact B-metric manifolds which are derived as a product of a real line and a 2-dimensional manifold equipped with a complex structure and a Norden metric. There are used two different methods for generation of the B-metric on the product manifold. The constructed manifolds are characterised with respect to the Ganchev-Mihova-Gribachev classification and their basic curvature properties.

math.DG↗
arXiv2015

Matrix Lie groups as 3-dimensional almost contact B-metric manifolds

The object of investigation are Lie groups considered as almost contact B-metric manifolds of the lowest dimension three. It is established a correspondence of all basic-class-manifolds of the Ganchev-Mihova-Gribachev classification of the studied manifolds and the explicit matrix representation of Lie groups. Some known Lie groups are equiped with almost contact B-metric structure of different types.

math.DG↗
arXiv2014

Almost contact B-metric structures and the Bianchi classification of the three-dimensional Lie algebras

The object of investigation are the almost contact manifolds with B-metric in the lowest dimension three, constructed on Lie algebras. It is considered a relation between the classes in the Bianchi classification of three-dimensional real Lie algebras and the classes of a classification of the considered manifolds. There are studied some geometrical characteristics in some special classes.

math.DG↗