. "Investigating manifolds with special structures from topological and geometric-analytical points of view"@en . "992"^^ . . . "differentiable manifold, multisymplectic form, G-structure, G2-structure, vector bundle"@en . . . "8"^^ . "8"^^ . . "0"^^ . "Variety se speci\u00E1ln\u00EDmi strukturami jsou v sou\u010Dasn\u00E9 dob\u011B aktivn\u011B studov\u00E1ny matematiky i fyziky. Maj\u00ED souvislost s fundament\u00E1ln\u00EDmi teoretick\u00FDmi ot\u00E1zkami geometrie a objevuj\u00ED se jako modely v teorii strun. Na\u0161e c\u00EDle jsou: 1. Nal\u00E9zt nutn\u00E9 a posta\u010Duj\u00EDc\u00ED podm\u00EDnky pro existenci uzav\u0159en\u00E9 G2-struktury (resp. ploch\u00E9 G2-struktury v dan\u00E9 kohomologick\u00E9 t\u0159\u00EDd\u011B) na 7-dimenzion\u00E1ln\u00ED variet\u011B. 2. Nal\u00E9zt glob\u00E1ln\u00ED invarianty uzav\u0159en\u00FDch G2-struktur. 3. Vy\u0161et\u0159ovat v\u00FD\u0161e uveden\u00E9 probl\u00E9my pro multi-symplektick\u00E9 formy v dimenz\u00EDch 6 a 8. 4. Nal\u00E9zt nutn\u00E9 a posta\u010Duj\u00EDc\u00ED podm\u00EDnky pro existenci symplektick\u00FDch nebo Kaehlerovych podvariet realizuj\u00EDc\u00EDch danou kohomologickou t\u0159\u00EDdu. 5. Vyvinout techniky pro \u0159e\u0161en\u00ED t\u011Bchto probl\u00E9m\u016F v obecn\u00E9m kontextu. N\u00E1\u0161 p\u0159\u00EDstup k tomuto probl\u00E9mu byl inspirov\u00E1n ned\u00E1vn\u00FDmi zji\u0161t\u011Bn\u00EDmi, \u017Ee nesta\u010D\u00ED pou\u017E\u00EDvat metody zn\u00E1m\u00E9 v sou\u010Dasn\u00E9 dob\u011B. Mus\u00ED existovat v\u011Bt\u0161\u00ED r\u00E1mec unifikuj\u00EDc\u00ED tyto probl\u00E9my a metody."@cs . "2007-01-01+01:00"^^ . "Studium variet se speci\u00E1ln\u00EDmi strukturami z topologickeho a geometricko-analytick\u00E9ho hlediska"@cs . "Manifolds with special structures are presently actively investigated by mathematicians and physicists. They are related to outstanding theoretical questions in geometry and appear as models in the string theory. Our aims are: 1. Finding necessary and sufficient conditions for the existence of a closed G2-structure (resp. a flat G2-structure among a given cohomology class) on a 7-manifold. 2. Finding global invariants of closed G2-structures. 3. Investigating the above problems for multi-symplectic forms in dimensions 6 and 8. 4. Finding necesary and sufficient conditions for the existence of symplectic or Kaehler submanifolds realizing a given homology class. 5. Develop techniques to deal with above problems in a general framework. Our main approach to this project has been guided by recent observations that it is not only possible to apply methods presently known. It must be here a bigger framework which unifies these problems and these methods."@en . . . "2010-12-31+01:00"^^ . . "0"^^ . "1"^^ . "992"^^ . .