About: Riemannian, pseudo-Riemannian and affine differential geometry

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An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Projekt, within Data Space : linked.opendata.cz associated with source document(s)

Attributes	Values
rdf:type	http://linked.opendata.cz/ontology/domain/vavai/Projekt
rdfs:seeAlso	http://www.isvav.cz/projectDetail.do?rowId=GAP201/11/0356
Description	1) Investigation of geodesic, holomorphically projective, F-planar, harmonic, conformal and related mappings, transformations and deformations on manifolds with affine connection, Riemannian, Hermitian and quaternionic spaces. Investigation of the torse-forming vector fields and their generalizations. Study of invariant decompositions of tensor spaces. Metrizability of connections, applications in the calculus of variations. 2) Finding of new classes of examples of pseudo-Riemannian manifolds (or affine manifolds, respectively) which are either semi-symmetric, or curvature homogeneous, or such that all geodesics on them are orbits of one-parameter groups of isometries (or affine diffeomorphisms, respectively). Study of natural geometries on tangent sphere bundles and their metric contact structures. Study of the modified curvature homogeneity (of type (1,3)) on Riemannian and pseudo-Riemannian manifolds. Relations to mathematical physics. 3) Classification of immersed surfaces in E3 whose Gauss-Mainardi-Codazzi equations are integrable in the sense of soliton theory. (en) 1) Studium geodetických, holomorfně-projektivních, F-planárních, 4-planárních, harmonických, konformních a dalších podobných zobrazení, transformací a deformací na varietách s afinní konexí, Riemannových, Hermitových a kvaternionových prostorech. Studium torso-formních vektorových polí a jejich zobecnění. Studium invariantních rozkladů tenzorových prostorů. Metrizovatelnost variet s afinní konexí, aplikace ve variačním počtu. 2) Nalezení nových tříd příkladů pseudo-Riemannových variet (resp. afinních variet), které jsou buďto semi-symetrické, nebo křivostně homogenní, nebo všechny jejich geodetiky jsou orbitami jednoparametrických grup izometrií (resp. afinních difeomorfizmů). Studium přirozených geometrií sférických tečných bandlů a jejich kontaktnich metrických struktur. Studium modifikované homogenní křivosti (typu (1,3)) na Riemannových a pseudo-Riemannových varietách. Souvislosti s matematickou fyzikou. 3) Klasifikace tříd vnořených ploch v E3, jejichž Gauss-Mainardi-Codazziho rovnice jsou integrabilní ve smyslu teorie solitonů.
Title	Riemannian, pseudo-Riemannian and affine differential geometry (en) Riemannova, pseudo-Riemannova a afinní diferenciální geometrie
skos:notation	GAP201/11/0356
http://linked.open...avai/cep/aktivita	Standard projects
http://linked.open...kovaStatniPodpora	http://linked.opendata.cz/resource/domain/vavai/projekt/GAP201%2F11%2F0356/celkovaStatniPodpora
http://linked.open...ep/celkoveNaklady	http://linked.opendata.cz/resource/domain/vavai/projekt/GAP201%2F11%2F0356/celkoveNaklady
http://linked.open...datumDodatniDoRIV	2014-07-01 (xsd:date)
http://linked.open...i/cep/druhSouteze	VS - Veřejná soutěž ve výzkumu a vývoji
http://linked.open...ep/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open.../cep/fazeProjektu	100269054
http://linked.open...ai/cep/hlavniObor	BA - Obecná matematika
http://linked.open...hodnoceniProjektu	V - Vynikající výsledky (s mezinárodním významem apod.). Zároveň byly splněny cíle a předpokládané výsledky uvedené ve smlouvě / rozhodnutí o poskytnutí podpory.
http://linked.open...vai/cep/kategorie	ZV - Základní výzkum
http://linked.open.../cep/klicovaSlova	Riemannian geometry pseudo-Riemannian geometry affine differential geometry integrable equation (en)
http://linked.open...ep/partnetrHlavni	Přírodovědecká fakulta
http://linked.open...inujicichPrijemcu	0 (xsd:int)
http://linked.open...cep/pocetPrijemcu	1 (xsd:int)
http://linked.open...ocetSpoluPrijemcu	2 (xsd:int)
http://linked.open.../pocetVysledkuRIV	80 (xsd:int)
http://linked.open...enychVysledkuVRIV	80 (xsd:int)
http://linked.open...lneniVMinulemRoce	2013-06-07 (xsd:date)
http://linked.open.../prideleniPodpory	http://linked.opendata.cz/resource/domain/vavai/cep/prideleniPodpory/P201-11-0356
http://linked.open...iciPoslednihoRoku	2013
http://linked.open...atUdajeProjZameru	2014
http://linked.open.../vavai/cep/soutez	SGA02011GA-ST
http://linked.open...usZobrazovaneFaze	DUU
http://linked.open...ai/cep/typPojektu	P - Projekt výzkumu a vývoje financovaný ze státního rozpočtu
http://linked.open...ep/ukonceniReseni	2013-12-31 (xsd:date)
http://linked.open...ep/zahajeniReseni	2011-01-01 (xsd:date)
http://linked.open...jektu+dodavatelem	The aims of the project were achieved. New results contributing to (pseudo)Riemannian geometry and the geometry of differential equations were published in 51 articles, among them 26 in IF journals, including high quality journals. 2 other articles are at referees. The project contributed also to education of PhD students. The budget of the project was used in accordance with the regulations. (en) Cíle projektu byly splněny. Projekt přinesl nové hodnotné výsledky z oblasti (pseudo)Riemannovy geometrie a geometrie diferenciálních rovnic. Přispěl též k vědecké výchově studentů. Výstupem je 51 prací publikovaných či přijatých k publikaci, z toho 26 v impaktovaných časopisech, včetně špičkových. Další 2 práce jsou v recenzním řízení. Čerpání finančních prostředků bylo v souladu s pravidly. (cs)
http://linked.open...tniCyklusProjektu	ZBKU
is http://linked.open...vavai/riv/projekt of	Eigenvalues of the Tachibana operator which acts on differential forms Toyoda's Theorem and Quasigroup Modes. Toyoda's Theorem and Quasigroup Modes ? ????????????? ???????????? ?????? ???????????? ????????? ???????????? Betti and Tachibana numbers of compact Riemannian manifolds Betti and Tachibana numbers Involutive birational transformations of arbitrary complexity in Euclidean spaces Integrable quantum Stäckel systems Golden section quasigroups, finite examples Golden section quasigroups, finite examples. On the rigidity of special holomorphically projective mapping. On a class of curvature preserving almost geodesic mappings of manifolds with affine connection On Holomorphically Projective Mappings with Certain Initial Conditions On Rings of Endomorphisms of Certain Free Modules On an application of the A-spaces over plural algebras in physics On composition of conformal and geodesic mappings between pseudo-Riemannian manifolds On scalar and total scalar curvatures of Riemann-Cartan manifolds On some applications of certain local algebras in physics On a class of curvature preserving almost geodesic mappings of manifolds with affine connection On holomorphically projective mappings with certain initial conditions On an application of the A-spaces over plural algebras in physics Rings of Endomorphisms of Certain Free Modules Invariance of the naturally lifted metrics on linear frame bundles over affine manifolds Almost Osserman structures on natural Riemann extensions Another integrable case in two-dimensional plasticity Lagrangian and Hamiltonian structures for the constant astigmatism equation Cnformally geodesic mappings satisfied the initial condition. Metrizable connections and restrictively variational connections in affine manifolds. Metrizable connections and restrictively variational connections in affine manifolds. Diagonalization of three-dimensional pseudo-Riemannian metrics In memory of Leonid Evtushik and Jan Kubarski Curvatures of the diagonal lift from an affine manifold to the linear frame bundle Holomorphically projective mappings of hyperbolically Kahler spaces preserving the Einstein tensor Hexagonal and Golden Quasigroups. Hexagonal and Golden Quasigroups. Recursion operators for dispersionless integrable systems in any dimension Projective Mappings and Dimensions of Vector Spaces of three types of Killing-Yano Tensors on Pseudo Riemannian Manifolds of Constant Curvature Pseudo-Riemannian manifolds modelled on symmetric spaces Rational involutive automorphisms related with standard representations of SL(2,R) Seven invariant classes of the Einstein equations and projective mappings Higher symmetries of cotangent coverings for Lax-integrable multi-dimensional partial differential equations and Lagrangian deformations Algebraic systems in cryptology and the security of information Coupling constant metamorphosis as an integrability-preserving transformation for general finite-dimensional dynamical systems and ODEs Conformal Klling vector field on a manifold with zero first Betti number Multiple Covariant Derivative and Decomposition Problems A Reciprocal Transformation for the Constant Astigmatism Equation A five-dimensional Riemannian manifold with an irreducible SO(3)-structure as a model of abstract statistical manifold A geodesic mapping and its field of symmetric linear endomorphisms On Lipschitz solutions of the constant astigmatism equation Oriented associativity equations and symmetry consistent conjugate curvilinear coordinate nets On Sinyukov's Equations in Their Relation to a Curvature Operator of Second Kind On dimensions of vector spaces of conformal Killing forms On canonical almost geodesic mappings of the first type of affinely connected spaces Possibilities of art therapy with parents of children with disabilities Bundle of projective normals for hyper-zone in non-Euclidean space The Projectivization of Conformal Models of Fibrations Determined by the Algebra of Quaternions Parallelogram Spaces and Medial Quasigroups Parallelogram spaces and medial quasigroups. On a Generalization of Curvature Homogeneous Spaces On metrizability of a class of 2-manifolds with linear connection On Holomorphically Projective Mappings From Manifolds With Equiaffine Connection Onto Kähler Manifolds On normals of manifolds in multidimensional projective space On pseudoconformal models of fibrations determined by the algebra of antiquaternions and projectivization of them On decomposition problems on manifolds with a special differential operator

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