Vojtěch Žádník

Preprints

10  Lie contact structures and chains, arXiv, 2009, 14 p.

We discuss possible equivalent views on Lie contact structures, among which a contact analogy of the description in 12 appears. This viewpoint is then used for the study of chains in the spirit of 6 and 7 ... pdf | more

Papers

12  Interactions between para-quaternionic and Grassmannian geometry, Ann. Global Anal. Geom., 2020, 27 p.

Almost para-quaternionic structures and almost Grassmannian structures of type (2,n) are basically the same. However, the clear prospect may be darkened by different tools and views used in respective communities. Here we confront several common topics including distinguished connections, curves and twistor constructions ... pdf | more

13  Conformal Patterson-Walker metrics, Asian J. Math., 2019, 32 p.

+ with Matthias Hammerl, Katja Sagerschnig, Josef Šilhan and Arman Taghavi-Chabert

This work partly covers and partly extends 11 by means of spinor calculus. Besides the characterization of the structure in question, Einstein metrics in the conformal class and infinitesimal symmetries are fully classified in underlying projective terms ... pdf | more

16  Conformal theory of curves with tractors, J. Math. Anal. Appl., 2019, 29 p.

+ with Josef Šilhan

Relative and absolute conformal invariants of generic curves, distinguished parametrizations, conformal geodesics and generalizations of all these concepts to null curves are studied via a tractor analogue of the classical Frenet frame construction ... pdf | more

14  Fefferman-Graham ambient metrics of Patterson-Walker metrics, Bull. Lond. Math. Soc., 2018, 5 p.

+ with Matthias Hammerl, Katja Sagerschnig, Josef Šilhan and Arman Taghavi-Chabert

Hanging around 11 and 13, we found that several nice geometric constructions meet in a nice way: the Fefferman-Graham ambient metric of a Patterson-Walker metric is itself a Patterson-Walker metric of the corresponding Thomas cone connection. Consequently, the ambient metric is given both in very global and very easy way ... pdf | more

11  A Projective-to-conformal Fefferman-type construction, SIGMA, 2017, 33 p.

+ with Matthias Hammerl, Katja Sagerschnig, Josef Šilhan and Arman Taghavi-Chabert

There is a natural conformal structure of split signature on the (weighted) cotangent bundle of a projective manifold. This is studied as a construction of Fefferman type which is, however, non-normal in general cases. Despite of this fact, we can keep a tight rein on the story ... pdf | more

9  Remarks on Grassmannian symmetric spaces, Arch. Math., 2008, 17 p.

+ with Lenka Zalabová

Non-flat Grassmannian (locally) symmetric spaces may exist only for type (2,n), respectively (n,2), in which cases the possible symmetries are heavily restricted. With a reference to 6 we discuss an example of such space that is globally symmetric ... pdf | more

8  Remarks on special symplectic connections, Arch. Math., 2008, 20 p.

+ with Martin Panák

Special symplectic connections are tightly related to parabolic contact structures, which both are fully classified. For three types of such connections, we offer a local realization due to an easy construction over the homogeneous model of the corresponding parabolic contact structure ... pdf | more

7  Contact projective structures and chains, Geom. Dedicata, 2010, 17 p.

+ with Andreas Čap

Chains again, but in this setting they behave quite differently. In particular, there is a subordinate (full) projective structure whose geodesics transverse to the contact distribution are just the chains of the contact projective structure ... pdf | more

6  On the geometry of chains, J. Differ. Geom., 2009, 33 p.

+ with Andreas Čap

For chains of integrable Lagrangean, respectively CR, contact manifold we can construct the corresponding normal Cartan connection directly, without any prolongation. Moreover, from these data, i.e. from the geometry of chains, the original geometric structure can be (almost) fully reconstructed ... pdf | more

5  Equations and symmetries of generalized geodesics, Proc. conf. DGA Prague, 2005, 14 p.

+ with Boris Doubrov

The notion of development of curves, symmetry algebras of model curves and the Cartan's method of moving frame allows one to derive the system of differential equations determining distinguished curves of given type. Point symmetries of such systems are discussed in detail for three prominent examples in the flat case ... pdf | more

4  Remarks on development of curves, Proc. 24th Winter School Srní, 2005, 10 p.

The development in the title means the one into the homogeneous model of a general Cartan geometry. We provide an alternative view on this classical notion (in terms of solutions to an equation involving the left logarithmic derivative) and add several applications ... pdf | more

2  Distinguished curves on 6-dimensional CR-manifolds of codimension 2, Proc. 23rd Winter School Srní, 2004, 12 p.

This is a direct application of the method from 1 and 3 to this slightly exotic geometric structure ... pdf | more

1  On distinguished curves in parabolic geometries, Transform. Groups, 2004, 24 p.

+ with Andreas Čap and Jan Slovák

This is an initiation to the systematic study of distinguished curves, their jets and parametrizations in parabolic geometries ... pdf | more

Thesis

3  Generalized geodesics, Masaryk University, 2004, 64 p.

The Ph.D. thesis on distinguished (or canonical) curves in parabolic geometries. Types of such curves are primarily stratified according to the grading of the background Lie algebra. The main problem concerns the specification of the order of the initial condition determining curves of respective types. The main instrument is the development into the homogeneous model ... pdf | more

Kniha

15  Václav Hlavatý (1894-1969). Cesta k jednotě, Munipress, 2017, 185 s.

+ s Helenou Durnovou a Janem Kotůlkem

Životopis významného českého a později amerického matematika zaplňuje jednu významnou mezeru mezi knihami tohoto žánru ... více

Osvěta

17  O křivkách a křivostech, Kvaternion, 2018, 12 s.

+ s Josefem Šilhanem

I v klasické a mnohokrát zpracované látce lze najít potemnělá zákoutí. V tomto příspěvku vyjasňujeme vztah mezi křivostmi křivky a objemy rovnoběžnostěnů určených několika derivovanými vektory, a to v obecné dimenzi, vzhledem k libovolné parametrizaci ... pdf | více

Výuka

g  Geometrie 3, IS, 2020

Zastřešení a doplnění předchozích kurzů: geometrická zobrazení, projektivní rozšíření, základní věty ... více

c  Geometrie 2, IS, 2013-19

Revize a zobecnění základních polohových a metrických pojmů, vztahů a odpovídajících skupin zobrazení pomocí vektorové algebry ... pdf | více

b  Geometrie 1, IS, 2013-20

Konstrukční geometrie: od klasických planimetrických úloh přes rozličné geometrické transformace k základním zobrazovacím metodám ... pdf | více

f  Vybrané partie z matematiky, IS, 2019

... zejména z geometrie: symetrie, stereometrie, kuželosečky a kvadriky ... více

e  Kuželosečky a kvadriky, IS, 2015-16

Několikerý pohled na kuželosečky a kvadriky: od elementárního vymezení po analytické, od názorných obrázků k algebraickým výpočtům ... pdf | více

d  Metody řešení matematických úloh, IS, 2014-19

Hledáme vhodné úlohy libovolné obtížnosti, při jejichž řešení se uplatní některé z pokročilejších poznatků a metod ... pdf | více

a  Neeukleidovské geometrie, IS, 2007-11

Od eukleidovské geometrie k absolutní a neeukleidovské, od polohových problémů k metrickým, od prvotních představ k reálným modelům ... pdf | více

Ostatní

Matematická olympiáda, MO, 2008-19

Editace zadání a komentářů pro kategorie Z, ročníky 58-69 ... pdf | více

Návodné úlohy a nápady ... více

Schůze, 2014-19

Nejdůležitější zápisy ze schůzí a státnic ... více

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Last update: Sep 3, 2020