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Mancho Manev

Publications and source records attributed to Mancho Manev.

At least 37 records · Page 2Linked to original sources
arXiv2018

Invariant tensors under the twin interchange of the pairs of the associated metrics on almost paracomplex pseudo-Riemannian manifolds

The object of study is almost paracomplex pseudo-Riemannian manifolds with a pair of metrics associated each other by the almost paracomplex structure. A torsion-free connection and tensors with geometric interpretation are found which are invariant under the twin interchange, i.e. the swap of the counterparts of the pair of associated metrics and the corresponding Levi-Civita connections. A Lie group depending on two real parameters is constructed as an example of a 4-dimensional manifold of the studied type and the mentioned invariant objects are found in an explicit form.

math.DG↗
arXiv2018

On Almost Paracontact Almost Paracomplex Riemannian Manifolds

Almost paracontact manifolds of an odd dimension having an almost paracomplex structure on the paracontact distribution are studied. The components of the fundamental (0,3)-tensor, derived by the covariant derivative of the structure endomorphism and the metric on the considered manifolds in each of the basic classes, are obtained. Then, the case of the lowest dimension 3 of these manifolds is considered. An associated tensor of the Nijenhuis tensor is introduced and the studied manifolds are characterized with respect to this pair of tensors. Moreover, cases of paracontact and para-Sasakian types are commented. A family of examples is given.

math.DG↗
arXiv2018

Two types of Lie Groups as 4-dimensional Riemannian manifolds with circulant structure

A 4-dimensional Riemannian manifold equipped with an endomorphism of the tangent bundle, whose fourth power is the identity, is considered. The matrix of this structure in some basis is circulant and the structure acts as an isometry with respect to the metric. Such manifolds are constructed on 4-dimensional real Lie groups with Lie algebras of two remarkable types. Some of their geometric characteristics are obtained.

math.DG↗
arXiv2017

On Geometry of Manifolds with Some Tensor Structures and Metrics of Norden Type

The object of study in the present dissertation are some topics in differential geometry of smooth manifolds with additional tensor structures and metrics of Norden type. There are considered four cases depending on the dimension of the manifold: 2n, 2n + 1, 4n and 4n + 3. The studied tensor structures, which are counterparts in the different related dimensions, are the almost complex/contact/hypercomplex structure and the almost contact 3-structure. The considered metric on the 2n-dimensional case is the Norden metric, and the metrics in the other three cases are generated by it. The purpose of the dissertation is to carry out the following: 1. Further investigations of almost complex manifolds with Norden metric including studying of natural connections with conditions for their torsion and invariant tensors under the twin interchange of Norden metrics. 2. Further investigations of almost contact manifolds with B-metric including studying of natural connections with conditions for their torsion and associated Schouten-van Kampen connections as well as a classification of affine connections. 3. Introducing and studying of Sasaki-like almost contact complex Riemannian manifolds. 4. Further investigations of almost hypercomplex manifolds with Hermitian-Norden metrics including studying of integrable structures of the considered type on 4-dimensional Lie algebra and tangent bundles with the complete lift of the base metric; introducing of associated Nijenhuis tensors in relation with natural connections having totally skew-symmetric torsion as well as quaternionic Kähler manifolds with Hermitian-Norden metrics. 5. Introducing and studying of manifolds with almost contact 3-structures and metrics of Hermitian-Norden type and, in particular, associated Nijenhuis tensors and their relationship with natural connections having totally skew-symmetric torsion.

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

Manifolds with almost contact 3-structure and metrics of Hermitian-Norden type

It is introduced a differentiable manifold with almost contact 3-structure which consists of an almost contact metric structure and two almost contact B-metric structures. The product of this manifold and a real line is an almost hypercomplex manifold with Hermitian-Norden metrics. It is proven that the introduced manifold of cosymplectic type is at. Some examples of the studied manifolds are given.

math.DG↗
arXiv2016

Natural Connections with Totally Skew-Symmetric Torsion on Manifolds with Almost Contact 3-Structure and Metrics of Hermitian-Norden Type

It is considered a differentiable manifold equipped with a pseudo-Riemannian metric and an almost contact 3-struc\-ture so that an almost contact metric structure and two almost contact B-metric structures are generated. There are introduced the so-called associated Nijenhuis tensors for the studied structures. It is given a geometric interpretation of the vanishing of these tensors as a necessary and sufficient condition for the existence of linear connections with totally skew-symmetric torsions preserving the structure. An example of a 7-dimensional manifold with connections of the considered type is given.

math.DG↗
arXiv2015

Associated Nijenhuis Tensors on Manifolds with Almost Hypercomplex Structures and Metrics of Hermitian-Norden Type

An associated Nijenhuis tensor of endomorphisms in the tangent bundle is introduced. Special attention is paid to such tensors for an almost hypercomplex structure and the metric of Hermitian-Norden type. There are studied relations between the six associated Nijenhuis tensors as well as their vanishing. It is given a geometric interpretation of the vanishing of these tensors as a necessary and sufficient condition for the existence of a unique connection with totally skew-symmetric torsion tensor. Similar idea is used in the paper of T. Friedrich and S. Ivanov in Asian J. Math. (2002) for some other structures. Finally, an example of a 4-dimensional manifold of the considered type with vanishing associated Nijenhuis tensors is given.

math.DG↗
arXiv2015

Pair of associated Schouten-van Kampen connections adapted to an almost contact B-metric structure

There are introduced and studied a pair of associated Schouten-van Kampen affine connections adapted to the contact distribution and an almost contact B-metric structure generated by the pair of associated B-metrics and their Levi-Civita connections. By means of the constructed non-symmetric connections, the basic classes of almost contact B-metric manifolds are characterized. Curvature properties of the considered connections are obtained.

math.DG↗
arXiv2015

Invariant Tensors under the Twin Interchange of Norden Metrics on Almost Complex Manifolds

The object of study are almost complex manifolds with a pair of Norden metrics, mutually associated by means of the almost complex structure. More precisely, a torsion-free connection and tensors with geometric interpretation are found which are invariant under the twin interchange, i.e. the swap of the counterparts of the pair of Norden metrics and the corresponding Levi-Civita connections. A Lie group depending on four real parameters is considered as an example of a 4-dimensional manifold of the studied type. The mentioned invariant objects are found in an explicit form.

math.DG↗
arXiv2014

On canonical-type connections on almost contact complex Riemannian manifolds

We consider a pair of smooth manifolds, which are the counterparts in the even-dimensional and odd-dimensional cases. They are separately an almost complex manifold with Norden metric and an almost contact manifolds with B-metric, respectively. They can be combined as the so-called almost contact complex Riemannian manifold. This paper is a survey with additions of results on differential geometry of canonical-type connections (i.e. metric connections with torsion satisfying a certain algebraic identity) on the considered manifolds.

math.DG↗
arXiv2014

Sasaki-like almost contact complex Riemannian manifolds

A Sasaki-like almost contact complex Riemannian manifold is defined as an almost contact complex Riemannian manifold which complex cone is a holomorphic complex Riemannian manifold. Explicit compact and non-compact examples are given. A canonical construction producing a Sasaki-like almost contact complex Riemannian manifold from a holomorphic complex Riemannian manifold is presented and called an $S^1$-solvable extension.

math.DG↗
arXiv2013

Canonical-type connection on almost contact manifolds with B-metric

The canonical-type connection on the almost contact manifolds with B-metric is constructed. It is proved that its torsion is invariant with respect to a subgroup of the general conformal transformations of the almost contact B-metric structure. The basic classes of the considered manifolds are characterized in terms of the torsion of the canonical-type connection.

math.DG↗
arXiv2013

Hypercomplex structures with Hermitian-Norden metrics on four-dimensional Lie algebras

Integrable hypercomplex structures with Hermitian and Norden metrics on Lie groups of dimension 4 are considered. The corresponding five types of invariant hypercomplex structures with hyper-Hermitian metric, studied by M.L. Barberis, are constructed here. The different cases regarding the signature of the basic pseudo-Riemannian metric are considered.

math.DG↗
arXiv2012

Almost contact B-metric manifolds with curvature tensors of Kähler type

On 5-dimensional almost contact B-metric manifolds, the form of any Kähler-type tensor (i.e. a tensor satisfying the properties of the curvature tensor of the Levi-Civita connection in the special class of the parallel structures on the manifold) is determined. The associated 1-forms are derived by the scalar curvatures of the Kähler-type tensor for the canonical connection on the manifolds from the main classes with closed 1-forms.

math.DG↗