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Mancho Manev

Publications and source records attributed to Mancho Manev.

At least 19 recordsLinked to original sources
arXiv2024

Ricci--Bourguignon Almost Solitons with Special Potential on Sasaki-like Almost Contact Complex Riemannian Manifolds

Almost contact complex Riemannian manifolds, also known as almost contact B-metric manifolds, are equipped with a pair of pseudo-Riemannian metrics that are mutually associated with each other using the tensor structure. Here we consider a special class of these manifolds, those of the Sasaki-like type. They have an interesting geometric interpretation: the complex cone of such a manifold is a holomorphic complex Riemannian manifold (also called a K\"ahler-Norden manifold). The basic metric on the considered manifold is specialized here as a soliton, i.e. has an additional curvature property such that the metric is a self-similar solution of an intrinsic geometric flow. Almost solitons are more general objects than solitons because they use functions rather than constants as coefficients in the defining condition. A $\beta$-Ricci-Bourguignon-like almost soliton ($\beta$ is a real constant) is defined using the pair of metrics. The introduced soliton is a generalization of some well-known (almost) solitons (such as those of Ricci, Schouten, and Einstein), which in principle arise from a single metric rather than a pair of metrics. The soliton potential is chosen to be pointwise collinear to the Reeb vector field, or the Lie derivative of any B-metric along the potential to be the same metric multiplied by a function. The resulting manifolds equipped with the introduced almost solitons are characterized geometrically. Appropriate examples for two types of almost solitons are constructed and the properties obtained in the theoretical part are confirmed.

math.DG↗
arXiv2023

Pairs of associated Yamabe almost solitons with vertical potential on almost contact complex Riemannian manifolds

Almost contact complex Riemannian manifolds, known also as almost contact B-metric manifolds, are in principle equipped with a pair of mutually associated pseudo-Riemannian metrics. Each of these metrics is specialized here as a Yamabe almost soliton with a potential collinear to the Reeb vector field. The resulting manifolds are then investigated in two important cases with geometric significance. The first is when the manifold is of Sasaki-like type, i.e. its complex cone is a holomorphic complex Riemannian manifold (also called a K\"ahler--Norden manifold). The second case is when the soliton potential is torse-forming, i.e. it satisfies a certain recurrence condition for its covariant derivative with respect to the Levi-Civita connection of the corresponding metric. The studied solitons are characterized. In the three-dimensional case, an explicit example is constructed and the properties obtained in the theoretical part are confirmed.

math.DG↗
arXiv2022

Yamabe Solitons on Conformal Almost Contact Complex Riemannian Manifolds with Vertical Torse-Forming Vector Field

A Yamabe soliton is considered on an almost contact complex Riemannian manifold (also known as an almost contact B-metric manifold) which is obtained by a contact conformal transformation of the Reeb vector field, its dual contact 1-form, the B-metric, and its associated B-metric. The case when the potential is a torse-forming vector field of constant length on the vertical distribution determined by the Reeb vector field is studied. In this way, manifolds from one of the main classes of the studied manifolds are obtained. The same class contains the conformally equivalent manifolds of cosymplectic manifolds by the usual conformal transformation of the given B-metric. An explicit 5-dimensional example of a Lie group is given, which is characterized in relation to the obtained results.

math.DG↗
arXiv2022

Almost Riemann Solitons with Vertical Potential on Conformal Cosymplectic Contact Complex Riemannian Manifolds

Almost Riemann solitons are introduced and studied on an almost contact complex Riemannian manifold, i.e. an almost contact B-metric manifold, obtained from a cosymplectic manifold of the considered type by a contact conformal transformation of the Reeb vector field, its dual contact 1-form, the B-metric, and its associated B-metric. The potential of the studied soliton is assumed to be in the vertical distribution, i.e. it is collinear to the Reeb vector field. In this way, manifolds from the four main classes of the studied manifolds are obtained. Curvature properties of the resulting manifolds are derived. An explicit example of dimension five is constructed. The Bochner curvature tensor is used (for dimension at least seven) as a conformal invariant to get properties and construct an explicit example in relation to the obtained results.

math.DG↗
arXiv2022

Redesign of web-based exam for knowledge evaluation in Advanced Mathematics for pharmaceutical students based on analysis of the results

The usage of the information technologies everywhere leads to demands for new manners of education. Modern e-learning environments lead the teaching, the learning and the evaluation of acquired knowledge and skills of the students to a new era. The students' motivation for e-learning is considered. The course of Advanced Mathematics is part of the curriculum of pharmaceutical students at the Medical University - Plovdiv. For students' knowledge evaluation it is used a hybrid-type exam in this university discipline, i.e. a problems-solving part and a remote web-based test which is created using the free and open-source e-educational platform Moodle. This paper presents a detailed analysis of the implemented electronic test for knowledge evaluation of the students, using statistical methods and instruments. The questions included in the test and the respective answers given by the students are estimated and analysed. Thus, it is made an improvement of the database of the test questions. The received results are used to enhance the quality of the developed knowledge evaluation and the type of its implementation.

cs.CY↗
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

Yamabe solitons on conformal Sasaki-like almost contact B-metric manifolds

A Yamabe soliton is defined on arbitrary almost contact B-metric manifold, which is obtained by a contact conformal transformation of the Reeb vector field, its dual contact 1-form, the B-metric, and its associated B-metric. The cases when the given manifold is cosymplectic or Sasaki-like are studied. In this way, manifolds from one of the main classes of the studied manifolds are obtained. The same class contains the conformally equivalent manifolds of cosymplectic manifolds by the usual conformal transformation of the B-metric. An explicit 5-dimensional example of a Lie group is given, which is characterized in relation to the obtained results.

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

Almost paracontact almost paracomplex Riemannian manifolds as extensions of 2-dimensional space-forms

Almost paracontact Riemannian manifolds of the lowest dimension are studied, whose paracontact distributions are equipped with an almost paracomplex structure. These manifolds are constructed as a product of a real line and a 2-dimensional Riemannian space-form. Their metric is obtained in two ways: as a cone metric and as a hyperbolic extension of the metric of the underlying paracomplex 2-manifold. The resulting manifolds are studied and characterized in terms of the classification used and their curvature properties.

math.DG↗
arXiv2021

Almost Ricci-like solitons with torse-forming vertical potential of constant length on almost contact B-metric manifolds

A generalization of Ricci-like solitons with torse-forming potential, which is a constant multiple of the Reeb vector field, is studied. The conditions under which these solitons are equivalent to almost Einstein-like metrics are given. Some results are obtained for a parallel symmetric second-order covariant tensor. Finally, an explicit example of an arbitrary dimension is given and some of the results are illustrated.

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↗
arXiv2020

Ricci-like solitons with arbitrary potential and gradient almost Ricci-like solitons on Sasaki-like almost contact B-metric manifolds

Ricci-like solitons with arbitrary potential are introduced and studied on Sasaki-like almost contact B-metric manifolds. It is proved that the Ricci tensor of such a soliton is the vertical component of both B-metrics multiplied by a constant. It is established that gradient almost Ricci-like solitons have constant soliton coefficients. Explicit examples of Lie groups as manifolds of dimensions 3 and 5 equipped with the structures studied are provided.

math.DG↗
arXiv2020

Ricci-like solitons with vertical potential on Sasaki-like almost contact B-metric manifolds

Ricci-like solitons on Sasaki-like almost contact B-metric manifolds are the object of study. Cases, where the potential of the Ricci-like soliton is the Reeb vector field or pointwise collinear to it, are considered. In the former case, the properties for a parallel or recurrent Ricci-tensor are studied. In the latter case, it is shown that the potential of the considered Ricci-like soliton has a constant length and the manifold is $η$-Einstein. Other curvature conditions are also found, which imply that the main metric is Einstein. After that, some results are obtained for a parallel symmetric second-order covariant tensor on the manifolds under study. Finally, an explicit example of dimension 5 is given and some of the results are illustrated.

math.DG↗
arXiv2019

Ricci-like solitons on almost contact B-metric manifolds

Ricci-like solitons with potential Reeb vector field are introduced and studied on almost contact B-metric manifolds. The cases of Sasaki-like manifolds and torse-forming potentials have been considered. In these cases, it is proved that the manifold admits a Ricci-like soliton if and only if the structure is Einstein-like. Explicit examples of Lie groups as 3- and 5-dimensional manifolds with the structures studied are provided.

math.DG↗